Chapter 5

Class 7 Mathematics · 113 questions · 110 with answers

Solved examples

example-1Multiple choice

The angles between North and East and North and West

(a)complementary angles
(b)supplementary angles
(c)both acute angles
(d)both obtuse angles

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Solution: Correct answer is (b). Fig. 5.1

example-2Multiple choice

Which of the following pair of angles are supplementary?

(a)48°, 42°
(b)60°, 60°
(c)75°, 105°
(d)179°, 2° A point name a location. .A point A A line is perfectly straight and extends line e, or for ever in both directions. A plane is a perfectly flat surface that plane p, or plane DEF extends forever in all directions. A segment, or line segment, is the part of a line between two points. A ray is part of a line that starts at one point and extends for ever in one direction. 15-04-2018

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Solution: Correct answer is (c).

example-3Multiple choice

In Fig. 5.2, a pair of corresponding angles is

(a)∠1, ∠2
(b)∠3, ∠6
(c)∠3, ∠5
(d)∠3, ∠7

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Solution: Correct answer is (d). Fig. 5.2

example-4Multiple choice

If two lines are intersected by a transversal, then the number of pairs of interior angles on the same side of the transversal is

(a)1
(b)2
(c)3
(d)4

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Solution: Correct answer is (b). An angle (∠) is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees, m∠l means the measure of ∠1. The angles can be named ∠XYZ, ∠1, or ∠Y. The vertex must be the middle letter. In Examples 5 to 7, fill in the blanks to make the statements true.

example-5Fill in the blanks

Two lines in a plane which never meet at any point are called _________.

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Solution: parallel lines

example-6Fill in the blanks

Angles of a linear pair are _________ as well as ________ .

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Solution: adjacent, supplementary

example-7Fill in the blanks

Adjacent angles have a common vertex, a common __________ and no-common _________.

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Solution: arm, interior points 15-04-2018 In Examples 8 to 11, state whether the statements are True or False.

example-8Short answer

Sum of two complementary angles is 180°.

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Solution: False

example-9Short answer

Sum of two supplementary angles is 180°.

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Solution: True

example-10Short answer

Sum of interior angles on the same side of a transversal with two parallel lines is 90°.

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Solution: False

example-11Short answer

Vertically opposite angles are equal.

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Solution: True

example-12Short answer

In Fig. 5.3, four line segments PQ, QR, RS and ST are making the letter W, PQ||RS and QR||ST. If angle between PQ and QR is 39°, find the values of x and y.

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Solution: Since PQ||RS and QR is transversal, so Fig. 5.3 x = 39° [Alternate interior angles] Again QR||ST and RS is a transversal. Therefore, y= x [Alternate interior angles] or y = 39°

example-13Short answer

In Fig. 5.4, are the angles 1 and 2 of the letter N forming a pair of adjacent angles? Give reasons.

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Solution: No, ∠1 and ∠2 are not forming a pair of adjacent angles as they do not have a common vertex. Fig. 5.4

example-14Multiple choice

In Fig. 5.5, the points A, O and B are collinear. Ray OC ⊥ ray OD. Check whether 15-04-2018

(i)∠AOD and ∠BOC are complementary,
(ii)∠AOC and ∠BOC are supplementary.

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Solution: Since points A, O and B are collinear Fig. 5.5 (Given), therefore AB is a straight line. (i) As O is a point on the line AB, therefore ∠AOD + ∠DOC + ∠BOC = 180° or, ∠AOD + ∠BOC + 90° = 180° or, ∠AOD + ∠BOC = 90° So, ∠AOD and ∠BOC are complementary angles. (ii) Also, ∠AOC and ∠BOC are supplementary as ∠AOC + ∠BOC = 180° A right angle measures 90°. An acute angle measures greater than 0° and less than 90°. An obtuse angle measures greater than 90° and less than 180°. Complementary angles are two angles whose measures add to 90°. Supplmentary angles are two angles whose measures add to 180°.

example-15Short answer

In Fig. 5.6 AB||EF, ED||CB and ∠APE is 39°. Find ∠CQF.

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Solution: Since ED||BC and AB is a transversal, so so ∠QBP = ∠APE [Corresponding angles] or ∠QBP = 39° Now, AB||EF and BC is a transversal. Therefore, ∠FQB = ∠QBP Fig. 5.6 [Alternate interior angles] 15-04-2018 or ∠FQB = 39° Also, ∠CQF + ∠FQB = 180° [Linear pair] So ∠CQF + 39° = 180° or ∠CQF = 180° – 39° or ∠CQF = 141°

example-16Short answer

Out of a pair of complementary angles, one is two-third of the other. Find the angles.

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Solution: Let one angle be x. So, other angle = 90° – x Thus, × x = 90° – x or 2x = 270° – 3x or 2x + 3x = 270° or 5x = 270° 270° or x= = 54° So, one angle = 54° and the other angle = 90° – 54°= 36°. Congruent figures have the same size and same shape. • Segments that have the same length are congruent. • Angles that have the same measure are congruent. • The symbol for congruence is ≅, which is read as “is congruent to.”

example-17Short answer

In Fig. 5.7, CD intersects the line AB at F, ∠CFB = 50° and ∠EFA = ∠AFD. Find the measure of ∠EFC.

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Solution: Let ∠EFA = x. Then ∠AFD = x. It is given that CD intersects line AB at F. Therefore, ∠CFB = ∠AFD (Vertically opposite angles) Fig. 5.7 So, x = 50° But ∠EFA = ∠AFD which gives ∠EFA = 50° 15-04-2018 Now ∠CFB + ∠EFA + ∠EFC = 180° [As AB is a straight line]. or, 50° + 50° + ∠EFC = 180° or, ∠EFC = 180° – 100° Thus, ∠EFC = 80°.

example-18Short answer

In the given figure, find out which pair of lines are parallel. Fig. 5.8

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Solution: Understand and Explore the Problem • What information is given in the question? Lines AB and CD are intersecting three lines EF, GH and KP at distinct points forming angles ∠1= 1230, ∠2 = 570, ∠3 = 550 and ∠5 = 1220. • What are you trying to find? We are trying to find (a) EF || GH or not 15-04-2018 (b) GH || KP or not (c) EF || KP or not (d) AB || CD or not Plan a Strategy (a) Since we want to find whether the lines are parallel or not, therefore recall the conditions when the lines are parallel. The lines are parallel if it satisfies any one of the following, (1) when corresponding angles are equal (2) when alternate interior angles are equal (3) when the sum of interior angles on the same side of the transversal is 180°. (b) Find out what type of angles are formed by lines EF, GH, KP taking AB or CD as transversal. Solve • For lines EF and GH, taking CD as transversal, ∠1 and ∠2 are interior angles on the same side of the transversal. Therefore, we check whether the sum of ∠1 and ∠2 is 180° or not. ∠1 = 123°, ∠2 = 57°, ∠1 + ∠2 = 123° + 57° = 180° Since the sum of interior ∠’s on the same side of the transversal is 180°, therefore EF || GH. • For lines GH and KP, taking CD as transversal, ∠2 and ∠3 are corresponding ∠’s. If these angles are equal, then lines are parallel. ∠2 = 57°, ∠3 = 55° ∠2 ≠∠3. Since corresponding angles are not equal, therefore, GH is not parallel to KP. • Similarly, for lines EF and KP, taking CD as transversal ∠1 and ∠3 are interior angles on the same side of the transversal. ∠1 = 123°, ∠3 = 55°, ∠1 + ∠3 = 123° + 55°=178°. Since the sum is not equal to 1800, therefore EF is not parallel to KP. • For lines AB and CD, taking GH as a transversal ∠2 = ∠4 = 57° (vertically opp. ∠’s). ∠5 and ∠4 are interior angles on the same side of the 15-04-2018 transversal and ∠5 + ∠4 = 122° + 57° = 179° ≠ 180°. Therefore, AB is not parallel to CD. Revise • EF||GH, since sum of interior ∠ ’s on the same side of transversal is 180°. • GH is not parallel to KP, since corresponding angles formed are not equal. • EF is not parallel to KP, since the sum of interior ∠’s on the same side of the transversal is not equal to 180°. • AB is not parallel to CD, since the sum of interior ∠’s on the same side of the transversal is not equal to 180°. 1. Can you find whether the lines EF, GH, KP, AB and CD are parallel or not by using other conditions of parallel lines? 2. Discuss with your classmates regarding their method towards this problem. In questions 1 to 41, there are four options out of which one is correct. Write the correct one. 1. The angles between North and West and South and East are (a) complementary (b) supplementary (c) both are acute (d) both are obtuse 2. Angles between South and West and South and East are (a) vertically opposite angles (b) complementary angles (c) making a linear pair (d) adjacent but not supplementary

Questions

Q1Multiple choice

Tell which statements are correct: If ∠X and ∠Y are congruent,

a.∠X = ∠Y
b.m∠X = m∠Y
c.∠X ≅ ∠Y.

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OSKNRKPNOV

Q2Short answer

Explain why vertically opposite angles must always be congruent.

Q3Multiple choice

In Fig. 5.9, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ ABC = 46°, then ∠ ABP is equal to

This question refers to a figure in the original PDF.

(a)44°
(b)67° Fig. 5.9
(c)13°
(d)62° 15-04-2018

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(b) 67° Fig. 5.9

Q4Multiple choice

If the complement of an angle is 79°, then the angle will be of

(a)1°
(b)11°
(c)79°
(d)101°

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(b) 11°

Q5Multiple choice

Angles which are both supplementary and vertically opposite are

(a)95°, 85°
(b)90°, 90°
(c)100°, 80°
(d)45°, 45°

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(b) 90°, 90°

Q6Multiple choice

The angle which makes a linear pair with an angle of 61° is of

(a)29°
(b)61°
(c)122°
(d)119°

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(d) 119°

Q7Multiple choice

The angles x and 90° – x are

(a)supplementary
(b)complementary
(c)vertically opposite
(d)making a linear pair

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(b) complementary

Q8Multiple choice

The angles x – 10° and 190° – x are

(a)interior angles on the same side of the transversal
(b)making a linear pair
(c)complementary
(d)supplementary

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(d) supplementary

Q9Multiple choice

In Fig. 5.10, the value of x is

This question refers to a figure in the original PDF.

(a)110°
(b)46°
(c)64°
(d)150°

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(d) 150°

Q10Multiple choice

In Fig. 5.11, if AB || CD, ∠ APQ = 50° and ∠PRD = 130°, then ∠ QPR is

This question refers to a figure in the original PDF.

(a)130°
(b)50°
(c)80°
(d)30° Fig. 5.10 Fig. 5.11 15-04-2018

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Q11Multiple choice

In Fig. 5.12, lines l and m intersect each other at a point. Which of the following is false?

This question refers to a figure in the original PDF.

(a)∠a = ∠b
(b)∠d = ∠c
(c)∠a + ∠d = 180°
(d)∠a = ∠d

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(d) ∠a = ∠d

Q12Multiple choice

If angle P and angle Q are supplementary and the measure of angle P is 60°, then Fig. 5.12 the measure of angle Q is

This question refers to a figure in the original PDF.

(a)120°
(b)60°
(c)30°
(d)20°

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(a) 120°

Q13Multiple choice

In Fig. 5.13, POR is a line. The value of

This question refers to a figure in the original PDF.

(a)40°
(b)45°
(c)55°
(d)60°

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(a) 40°

Q14Multiple choice

In Fig. 5.14, POQ is a line. If x = 30°, then ∠ QOR is Fig. 5.13 Fig. 5.14

This question refers to a figure in the original PDF.

(a)90°
(b)30°
(c)150°
(d)60° If two parallel lines are intersected by a transversal, corresponding angles are congurent, • alternate interior angles are congruent • and alternate exterior angles are congruent. If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent to 90° angles. 15-04-2018

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(a) 90°

Q15Multiple choice

The measure of an angle which is four times its supplement is

(a)36°
(b)144°
(c)16°
(d)64°

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(b) 144°

Q16Multiple choice

In Fig. 5.15, the value of y is

This question refers to a figure in the original PDF.

(a)30°
(b)15°
(c)20°
(d)22.5° Fig. 5.15

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Q17Multiple choice

In Fig. 5.16, PA || BC || DT and AB || DC. Then, the values of a and b are respectively. Fig. 5.16

This question refers to a figure in the original PDF.

(a)60°, 120°
(b)50°,130°
(c)70°,110°
(d)80°,100°

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(b) 50°,130°

Q18Multiple choice

The difference of two complementary angles is 30°. Then, the angles

(a)60°, 30°
(b)70°, 40°
(c)20°,50°
(d)105°,75°

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(a) 60°, 30°

Q19Multiple choice

In Fig. 5.17, PQ || SR and SP || RQ. Then, angles a and b are respectively

This question refers to a figure in the original PDF.

(a)20°, 50°
(b)50°, 20°
(c)30°,50°
(d)45°, 35° Fig. 5.17

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(a) 20°, 50°

Q20Multiple choice

In Fig. 5.18, a and b are

This question refers to a figure in the original PDF.

(a)alternate exterior angles
(b)corresponding angles
(c)alternate interior angles
(d)vertically opposite angles

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Q21Multiple choice

If two supplementary angles are in the ratio 1 : 2, then the bigger angle is

This question refers to a figure in the original PDF.

(a)120°
(b)125°
(c)110°
(d)90° Fig. 5.18 15-04-2018

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(a) 120°

Q22Multiple choice

In Fig. 5.19, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠ QOS measures

This question refers to a figure in the original PDF.

(a)150°
(b)75°
(c)45°
(d)60°

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(b) 75°

Q23Multiple choice

Statements a and b are as given Fig. 5.19 below: a : If two lines intersect, then the vertically opposite angles are equal. b : If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. Then

This question refers to a figure in the original PDF.

(a)Both a and b are true
(b)a is true and b is false
(c)a is false and b is true
(d)both a and b are false

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(b) a is true and b is false

Q24Multiple choice

For Fig. 5.20, statements p and q are given below: p : a and b are forming a linear pair. q : a and b are forming a pair of adjacent angles. Then,

This question refers to a figure in the original PDF.

(a)both p and q are true
(b)p is true and q is false
(c)p is false and q is true
(d)both p and q are false Fig. 5.20 A transversal is a line that intersects two or more lines that lie in the same plane in distinct points. Transversals to parallel lines form angles with special properties. Alternate interior Alternate exterior Corresponding 15-04-2018

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(a) both p and q are true

Q25Multiple choice

In Fig. 5.21, ∠AOC and ∠ BOC form a pair of

This question refers to a figure in the original PDF.

(a)vertically opposite angles
(b)complementary angles
(c)alternate interior angles
(d)supplementary angles

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(d) supplementary angles

Q26Multiple choice

In Fig. 5.22, the value of a is Fig. 5.21

This question refers to a figure in the original PDF.

(a)20°
(b)15°
(c)5°
(d)10°

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(d) 10°

Q27Multiple choice

In Fig. 5.23, if QP || SR, the value of a is

This question refers to a figure in the original PDF.

(a)40°
(b)30°
(c)90°
(d)80° Fig. 5.22 Fig. 5.23

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Q28Multiple choice

In which of the following figures, a and b are forming a pair of adjacent angles?

This question refers to a figure in the original PDF.

(a)
(b)
(c)
(d)Fig. 5.24 15-04-2018 1. Tell how many different angles would be formed by a transversal intersecting three parallel lines. How many different angle measures would there be? 2. Explain how a transversal could intersect two other lines so that corresponding angles are not congruent.

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(d) Fig. 5.24 15-04-2018 1. Tell how many different angles would be formed by a transversal intersecting three parallel lines. How many different angle measures would there be? 2. Explain how a transversal could intersect two other lines so that corresponding angles are not congruent.

Q29Multiple choice

In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) uncommon arms are always opposite rays Then

(a)All (i), (ii) and (iii) are true
(b)(iii) is false
(c)(i) is false but (ii) and (iii) are true
(d)(ii) is false

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(b) (iii) is false

Q30Multiple choice

In Fig. 5.25, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to

This question refers to a figure in the original PDF.

(a)126°
(b)144°
(c)136°
(d)154° Fig. 5.25 Words Numbers Algebra The angle measures of a triangle add to 180°. 43° + 58° + 79° = 180° r° + s° + t° = 180° 15-04-2018

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(b) 144°

Q31Multiple choice

In Fig. 5.26, POQ is a line, then a is equal to

This question refers to a figure in the original PDF.

(a)35°
(b)100°
(c)80°
(d)135°

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Q32Multiple choice

Vertically opposite angles are always

This question refers to a figure in the original PDF.

(a)supplementary
(b)complementary
(c)adjacent Fig. 5.26
(d)equal

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(d) equal

Q33Multiple choice

In Fig. 5.27, a = 40°. The value of b is

This question refers to a figure in the original PDF.

(a)20°
(b)24°
(c)36°
(d)120°

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(a) 20°

Q34Multiple choice

If an angle is 60° less than two times of its supplement, then the greater angle is Fig. 5.27

This question refers to a figure in the original PDF.

(a)100°
(b)80°
(c)60°
(d)120°

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(a) 100°

Q35Multiple choice

In Fig. 5.28, PQ || RS. If ∠1=(2a+b)° and ∠6=(3a–b)°, then the measure of ∠2 in terms of b is

This question refers to a figure in the original PDF.

(a)(2+b)°
(b)(3–b)°
(c)(108–b)°
(d)(180–b)°

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Q36Multiple choice

In Fig. 5.29, PQ||RS and a : b = 3 : 2. Then, f is equal to

This question refers to a figure in the original PDF.

(a)36°
(b)108°
(c)72°
(d)144° Fig. 5.28 Fig. 5.29 15-04-2018 An acute triangle has 3 acute angles. A right triangle has 1 right angle, An obtuse triangle has 1 obtuse angle. An e quilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

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(b) 108°

Q37Multiple choice

In Fig. 5.30, line l intersects two parallel lines PQ and RS. Then, which one of the following is not true?

This question refers to a figure in the original PDF.

(a)∠1 = ∠3
(b)∠2 = ∠4
(c)∠6 = ∠7
(d)∠4 = ∠8

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(d) ∠4 = ∠8

Q38Multiple choice

In Fig. 5.30, which one of the following is not true?

This question refers to a figure in the original PDF.

(a)∠1 + ∠5 = 180°
(b)∠2 + ∠5 = 180°
(c)∠3 + ∠8 = 180°
(d)∠2 + ∠3 = 180°

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(d) ∠2 + ∠3 = 180°

Q39Multiple choice

In Fig. 5.30, which of the following is true? Fig. 5.30

This question refers to a figure in the original PDF.

(a)∠1 = ∠5
(b)∠4 = ∠8
(c)∠5 = ∠8
(d)∠3 = ∠7 1. Explain whether a right triangle can be equilateral. Can it be isosceles? scalene? 2. Explain whether a triangle can have two right angles. Can it have two obtuse angles?

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Q40Multiple choice

In Fig. 5.31, PQ||ST. Then, the value of x + y is

This question refers to a figure in the original PDF.

(a)125°
(b)135°
(c)145°
(d)120° Fig. 5.31 15-04-2018

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(b) 135°

Q41Multiple choice

In Fig. 5.32, if PQ||RS and QR||TS, then the value a is

This question refers to a figure in the original PDF.

(a)95°
(b)90°
(c)85°
(d)75° Fig. 5.32 In questions 42 to 56, fill in the blanks to make the statements true.

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(a) 95°

Q42Fill in the blanks

If sum of measures of two angles is 90°, then the angles are _________.

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Complementary

Q43Fill in the blanks

If the sum of measures of two angles is 180°, then they are _________.

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Supplementary

Q44Fill in the blanks

A transversal intersects two or more than two lines at _________ points. If a transversal intersects two parallel lines, then (Q. 45 to 48).

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Distinct

Q45Short answer

sum of interior angles on the same side of a transversal is .

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1800

Q46Short answer

alternate interior angles have one common .

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Arm

Q47Short answer

corresponding angles are on the side of the transversal.

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Same

Q48Short answer

alternate interior angles are on the side of the transversal.

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Opposite

Q49Short answer

Two lines in a plane which do not meet at a point anywhere are called lines.

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Parallel

Q50Fill in the blanks

Two angles forming a __________ pair are supplementary.

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Linear

Q51Fill in the blanks

The supplement of an acute is always __________ angle.

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Obtuse

Q52Fill in the blanks

The supplement of a right angle is always _________ angle.

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Right angle

Q53Fill in the blanks

The supplement of an obtuse angle is always _________ angle.

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Acute

Q54Fill in the blanks

In a pair of complementary angles, each angle cannot be more than _________90°.

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900

Q55Fill in the blanks

An angle is 45°. Its complementary angle will be __________ .

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450

Q56Fill in the blanks

An angle which is half of its supplement is of __________. In questions 57 to 71, state whether the statements are True or False.

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600

Q57Short answer

Two right angles are complementary to each other. 15-04-2018

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False

Q58Short answer

One obtuse angle and one acute angle can make a pair of complementary angles.

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False

Q59Short answer

Two supplementary angles are always obtuse angles.

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False

Q60Short answer

Two right angles are always supplementary to each other.

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True

Q61Short answer

One obtuse angle and one acute angle can make a pair of suplementary angles.

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True

Q62Short answer

Both angles of a pair of supplementary angles can never be acute angles.

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True

Q63Short answer

Two supplementary angles always form a linear pair.

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False

Q64Short answer

Two angles making a linear pair are always supplementary.

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True

Q65Short answer

Two angles making a linear pair are always adjacent angles.

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True

Q66Short answer

Vertically opposite angles form a linear pair.

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False

Q67Short answer

Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles.

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False

Q68Short answer

Vertically opposite angles are either both acute angles or both obtuse angles.

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True

Q69Short answer

A linear pair may have two acute angles.

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False

Q70Short answer

An angle is more than 45°. Its complementary angle must be less than 45°.

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True

Q71Short answer

Two adjacent angles always form a linear pair.

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False

Q72Multiple choice

Write down each pair of adjacent angles shown in the following figures:

This question refers to a figure in the original PDF.

(i)
(ii)
(iii)
(iv)Fig. 5.33 15-04-2018

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(i)

(ii)

(iii)

(iv) Fig. 5.33 15-04-2018

Q73Multiple choice

In each of the following figures, write, if any,

This question refers to a figure in the original PDF.

(i)each pair of vertically opposite angles, and
(ii)each linear pair. (i) (ii)
(iii)
(iv)Fig. 5.34

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(i) each pair of vertically opposite angles, and

(ii) each linear pair. (i) (ii)

(iii)

(iv) Fig. 5.34

Q74Multiple choice

Name the pairs of supplementary angles in the following figures:

This question refers to a figure in the original PDF.

(i)
(ii)
(iii)Fig. 5.35 15-04-2018

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(i)

(ii)

(iii) Fig. 5.35 15-04-2018

Q75Short answer

In Fig. 5.36, PQ || RS, TR || QU and ∠PTR = 42°. Find ∠QUR. Fig. 5.36

This question refers to a figure in the original PDF.

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∠QUR = 138°

Q76Multiple choice

The drawings below (Fig. 5.37), show angles formed by the goalposts at different positions of a football player. The greater the angle, the better chance the player has of scoring a goal. For example, the player has a better chance of scoring (ii) a goal from Position A than from Position B. (i) (iii) Fig. 5.37 In Parts

This question refers to a figure in the original PDF.

(a)and
(b)given below it may help to trace the diagrams and draw and measure angles. (a) Seven football players are practicing their kicks. They are lined up in a straight line in front of the goalpost [Fig.(ii)]. Which player has the best (the greatest) kicking angle? (b) Now the players are lined up as shown in Fig. (iii). Which player has the best kicking angle?
(c)Estimate atleast two situations such that the angles formed by different positions of two players are complement to each other.

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(a) and

(b) given below it may help to trace the diagrams and draw and measure angles. (a) Seven football players are practicing their kicks. They are lined up in a straight line in front of the goalpost [Fig.(ii)]. Which player has the best (the greatest) kicking angle? (b) Now the players are lined up as shown in Fig. (iii). Which player has the best kicking angle?

(c) Estimate atleast two situations such that the angles formed by different positions of two players are complement to each other.

Q77Short answer

The sum of two vertically opposite angles is 166°. Find each of the angles. 15-04-2018

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83°

Q78Short answer

In Fig. 5.38, l ||m || n. ∠ QPS = 35° and ∠ QRT = 55°. Find ∠PQR.

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90°

Q79Multiple choice

In Fig. 5.39, P, Q and R are collinear points and TQ ⊥ PR, Name;

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(a)pair of complementary angles
(b)two pairs of supplementary angles.
(c)four pairs of adjacent angles. Fig. 5.38 Fig. 5.39

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(a) pair of complementary angles

(b) two pairs of supplementary angles.

Q80Multiple choice

In Fig. 5.40, OR ⊥ OP.

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(i)Name all the pairs of adjacent angles.
(ii)Name all the pairs of complementary angles.

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(i) Name all the pairs of adjacent angles.

(ii) Name all the pairs of complementary angles.

Q81Multiple choice

If two angles have a common vertex and their arms form Fig. 5.40 opposite rays (Fig. 5.41), Then,

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(a)how many angles are formed?
(b)how many types of angles are formed?
(c)write all the pairs of vertically opposite angles.

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(a) how many angles are formed?

(b) how many types of angles are formed?

Q82Multiple choice

In (Fig 5.42) are the following pairs of angles adjacent? Justify your answer. Fig. 5.41 15-04-2018

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(i)
(ii)
(iii)
(iv)Fig. 5.42

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(i)

(ii)

(iii)

(iv) Fig. 5.42

Q83Short answer

In Fig. 5.43, write all the pairs of supplementary angles. Fig. 5.43

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∠ ∠7, ∠2; ∠1, ∠8; ∠5, ∠6; ∠6, ∠3; ∠3, ∠4; ∠4, ∠5

Q84Multiple choice

What is the type of other angle of a linear pair if

(a)one of its angle is acute?
(b)one of its angles is obtuse?
(c)one of its angles is right?

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(a) one of its angle is acute?

(b) one of its angles is obtuse?

Q85Short answer

Can two acute angles form a pair of supplementary angles? Give reason in support of your answer.

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Q86Short answer

Two lines AB and CD intersect at O (Fig. 5.44). Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only. 15-04-2018 Fig. 5.44 Polygon Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 n-gon n

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∠1, ∠2; ∠2, ∠3; ∠3, ∠4; ∠4, ∠1.

Q87Short answer

If the complement of an angle is 62°, then find its supplement.

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152°

Q88Short answer

A road crosses a railway line at an angle of 30° as shown in Fig.5.45. Find the values of a, b and c. Fig. 5.45 15-04-2018

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∠a = 30°, ∠b = 150°, ∠c = 150°

Q89Short answer

The legs of a stool make an angle of 35° with the floor as shown in Fig. 5.46. Find the angles x and y. Fig. 5.46

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∠x = 35°, ∠y = 145°

Q90Multiple choice

Iron rods a, b, c, d, e and f are making a design in a bridge as shown in Fig. 5.47, in which a ||b, c ||d, e || f. Find the marked angles between

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(i)b and c
(ii)d and e
(iii)d and f
(iv)c and f Fig. 5.47

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(i) b and c

(ii) d and e

(iii) d and f

(iv) c and f Fig. 5.47

Q91Short answer

Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in Fig. 5.48 and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles. Fig. 5.48 15-04-2018

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∠ ∠x = 60°, ∠y = 120°, ∠z = 60°

Q92Short answer

In Fig. 5.49, AB||CD, AF||ED, ∠AFC = 68° and ∠FED = 42°. Find ∠EFD. Fig. 5.49

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∠EFD = 70°

Q93Short answer

In Fig. 5.50, OB is perpendicular to OA and ∠BOC = 49°. Find ∠AOD. Fig. 5.50

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∠AOD = 139°

Q94Short answer

Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Fig. 5.51), find ∠COF. Fig. 5.51

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110°

Q95Short answer

Measures (in degrees) of two complementary angles are two consecutive even integers. Find the angles.

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440, 46°

Q96Short answer

If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles. 15-04-2018

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100°, 80° OSKNRKPNOV

Q97Short answer

Two angles are making a linear pair. If one of them is one-third of the other, find the angles.

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45°, 135°

Q98Short answer

Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.

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89°, 91°

Q99Short answer

In Fig. 5.52, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE. Fig. 5.52

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60°, 120°

Q100Short answer

In Fig. 5.53, find the value of ∠BOC, if points A, O and B are collinear. Fig. 5.53

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40°

Q101Short answer

In Fig. 5.54, if l ||m, find the values of a and b. Fig. 5.54 15-04-2018

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67°, 48°

Q102Short answer

In Fig. 5.55, l || m and a line t intersects these lines at P and Q, respectively. Find the sum 2a + b. Fig. 5.55

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396°

Q103Short answer

In Fig. 5.56, QP || RS. Find the values of a and b. Fig. 5.56

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65°, 70°

Q104Short answer

In Fig. 5.57, PQ || RT. Find the value of a + b. Fig. 5.57

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100°

Q105Multiple choice

In Fig 5.58, PQ, RS and UT are parallel lines.

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(i)If c = 570 and a = , find the value of d. Fig. 5.58
(ii)If c = 75 and a = c, find b. 15-04-2018

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(i) If c = 570 and a = , find the value of d. Fig. 5.58

(ii) If c = 75 and a = c, find b. 15-04-2018

Q106Short answer

In Fig. 5.59, AB||CD . Find the reflex ∠ EFG. Fig. 5.59 Look for a pattern between the number of sides and the number of triangles.

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281°

Q107Short answer

In Fig. 5.60, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y. Fig. 5.60

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114°, 132°

Q108Short answer

In Fig. 5.61, l, m and n are parallel lines, and the lines p and q are also parallel. Find the values of a, b and c. Fig. 5.61 15-04-2018

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20°, 40°, 30°

Q109Short answer

In Fig. 5.62, state which pair of lines are parallel. Give reason. Fig. 5.62

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m || n.

Q110Multiple choice

In Fig. 5.63, examine whether the following pairs of lines are parallel or not:

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(i)EF and GH
(ii)AB and CD Fig. 5.63

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(i) EF and GH

(ii) AB and CD Fig. 5.63

Q111Short answer

In Fig. 5.64, find out which pair of lines are parallel: Fig. 5.64 15-04-2018

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EF || GH 113. 110°, 100° 2. OSKNRKPNOV

Q112Multiple choice

In Fig. 5.65, show that

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(i)AB || CD
(ii)EF || GH Fig. 5.65

Q113Multiple choice

In Fig. 5.66, two parallel lines l and m are cut by two transversals p and q. Determine the values of x and y. Fig. 5.66 1. The game pool belongs to billiard sports and generally played with a cue stick which is used to strike billiard balls, moving them around a cloth-covered billiards table with six pocket bounded by rubber cushions. The angle at which a pool ball hits the side of a table has the same 15-04-2018 measure as the angle at which it bounces off the side. This is shown in the drawing at the right. The marked angles have the same measure, and the arrow shows the ball’s path. In Parts

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(a)–(c), trace the drawing. Then use your protractor to find the path the ball will take when it bounces off the side. Tell whether the ball will go into a pocket or hit another side. (Draw just one bounce.) (a) When light hits a mirror, it behaves in the same way as a pool ball hitting the side of a table. If light hits a mirror at an angle, it bounces off at the same angle. In physics, this law is often
(b)stated as “the angle of incidence = the angle of reflection.”
(c)
(d)Try to trace this drawing. Draw a path for which the ball will bounce off a side and land in the lower-right pocket. 15-04-2018 2. Crossword Puzzle Fill the crossword puzzle with the help of following clues: Across 1. Two lines in a plane which do not intersect each other. 2. A pair of adjacent angles having their non common arms opposite rays. 3. A pair of angles having a common vertex, a common arm and their interiors do not overlap. 4. The two lines are intersected by a line at distinct points. 5. The sum of two angles is 90°. Down 6. Sum of two angles is 180°. 7. The two lines in a plane intersect each other at one and only one point are called _________ . 8. When two parallel lines intersected by a transversal at two distinct points then the _________ angles are equal. 15-04-2018