RD SHARMA SOLUTION CHAPTER – 10 Lines and Angles | CLASS 9TH MATHEMATICS-EDUGROWN

Table of Contents

Chapter 10 – Lines and Angles Exercise Ex. 10.1

Question 1

Write the complement of each of the following angles:

(i) 20^o

(ii) 35^o

(iii) 90^o

(iv) 77^o

(v) 30^oSolution 1

Question 2

Write the supplement of each of the following angles:

(i) 54^o

(ii) 132^o

(iii) 138^oSolution 2

(i) 54°

Since, the sum of an angle and its supplement is 180°

∴Its supplement will be 180° – 54° = 126°.

(ii) 132°

Since, the sum of an angle and its supplement is 180°

∴Its supplement will be 180° – 132° = 48°.

(iii) 138°

Since, the sum of an angle and its supplement is 180°

∴Its supplement will be 180° – 138° = 42°.Question 3

If an angle is 28^o less than its complement, find its measure.Solution 3

Question 4

If an angle is 30^o more than one half of its complement, find the measure of the angle.Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of angle.Solution 13

Let the measure of the angle be x^o.

Its complement will be (90^o – x^o) and its supplement will be (180^o – x^o).

Supplement of thrice of the angle = (180^o – 3x^o)

According to the given information:

(90^o – x^o) = (180^o – 3x^o)

3x – x = 180 – 90

2x = 90

x = 45

Thus, the measure of the angle is 45^o.

The measure of the angle is 45^oQuestion 14

Solution 14

Chapter 10 – Lines and Angles Exercise Ex. 10.2

Question 1

In fig., OA and OB are opposite rays:

(i) If x = 25°, what is the value of y?

(ii) if y = 35°, what is the value of x?

Solution 1

Question 2

In fig., write all pairs of adjacent angles and all the linear pairs.

Solution 2

Question 3

In fig., find x. further find ∠BOC, ∠COD and ∠AOD

Solution 3

Question 4

In fig., rays OA, OB, OC, OD and OE have the common end point O. Show that ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360ºSolution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

How many pairs of adjacent angles, in all, can you name in fig.

Solution 7

Question 8

In fig., determine the value of x.

Solution 8

Question 9

In fig., AOC is a line, find x.

Solution 9

Question 10

In Fig., POS is a line, find x.

Solution 10

Question 11

In fig., ACB is a line such that ∠DCA = 5x and ∠DCB = 4x. Find the values of ∠DCA and∠DCB

Solution 11

Question 12

Give POR = 3x and QOR = 2x + 10, find the value of x for which POQ will be aline.

Solution 12

Question 13

What value of y would make AOB a line in fig., if ∠AOC = 4y and ∠BOC = (6y + 30)?

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

In Fig., Lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5:7, find all the angles.

Solution 16

Question 17

In Fig. If a greater than b by one third of a right-angle. find the values of a and b.

Solution 17

Question 18

Solution 18

Question 19In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that

Solution 19Given that OR ⊥ PQ ∴ POR = 90^o ⇒ ∠POS + ∠SOR = 90^o ∠ROS = 90^o – ∠POS … (1) ∠QOR = 90^o (As OR ⊥ PQ) ∠QOS – ∠ROS = 90^o ∠ROS = ∠QOS – 90^o … (2) On adding equations (1) and (2), we have 2 ∠ROS = ∠QOS – ∠POS

Chapter 10 – Lines and Angles Exercise Ex. 10.3

Question 1

In fig., lines l₁ aans l₂ intersect at O, forming angles as shown in the figure. If x = 45, find the values of y, z and u.

Solution 1

Question 2

In fig., three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of x, y, z and u.

Solution 2

Question 3

In fig. , find the values of x, y and z.

Solution 3

Question 4

In Fig., find the value of X.

Solution 4

Question 5

Solution 5

Question 6

In fig., rays AB and CD intersect at O.

(i) Determine y when x = 60^o

(ii) Determine x when y = 40

Solution 6

Question 7

In fig., lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠COF, ∠DOE and ∠BOF.

Solution 7

Question 8

Solution 8

Question 9

In fig., lines AB, and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

Solution 9

Question 10

Which of the following statements are true (T) and which are false (F)?

(i) Angles forming a linear pair are supplementary.

(ii) If two adjacent angles are equal, then each angle measures 90^o.

(iii) Angles forming a linear pair can both be acute angles.

(iv) If angles forming a linear pair are equal, then each of these angles is of measure 90^o.Solution 10

(i) True

(ii) False

(iii) False

(iv) TrueQuestion 11

Fill in the blanks so as to make the following statements true:

(i) If one angle of a linear pair is acute, then its other angle will be ________.

(ii) A ray stands on a line, then the sum of the two adjacent angles so formed is _______.

(iii) If the sum of two adjacent angles is 180^o, then the ______ arms of the two angles are opposite rays.Solution 11

(i) obtuse.

(ii) 180^o

(iii) uncommonQuestion 12

Solution 12

Question 13

Solution 13

Chapter 10 – Lines and Angles Exercise Ex. 10.4

Question 1

In fig., AB ∥ CD and ∠1 and ∠2 are in the ratio 3:2. determine all angles from 1 to 8.

Solution 1

Question 2

In fig., l, m and n are parallel lines intersected by transversal p at x, y and z respectively. find ∠1, ∠2, ∠3.

Solution 2

Question 3

In fig., if AB ∥ CD and CD ∥ EF, find ∠ACE.

Solution 3

Question 4

In fig., state which lines are parallel and why.

Solution 4

Question 5

In fig. if l ∥ m, n ∥ p and ∠1 = 85°, find ∠2.

Solution 5

Question 6

If two straight lines are perpendicular to the same line, prove that they are parallel to each other.Solution 6

Question 7

Solution 7

Question 8

Solution 8

Let AB and CD be perpendicuar to line MN.

Question 9

In fig., ∠1 = 60° and ∠2 = (2/3)^rd of a right angle. prove that l ∥ m

Solution 9

Question 10

In fig., if l ∥ m ∥ n and ∠1 = 60°, find ∠2.

Solution 10

Question 11

Solution 11

Let AB and CD be perpendicuar to line MN.

Question 12

Solution 12

Question 13

Solution 13

Question 14

In fig., p is transversal to lines m and n, ∠2 = 120° and ∠5 = 60°. Prove that m ∥ n.

Solution 14

Question 15

In fig., transceral l intersects two lines m and n, ∠4 = 110° and ∠7 = 65°. is m ∥ n ?

Solution 15

Question 16

Which pair of lines in Fig., are parallel? give reasons.

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

In fig., AB ∥ CD ∥ EF and GH ∥ KL. Find ∠HKL

Solution 20

Question 21

In fig., show that AB ∥ EF.

Solution 21

Question 22

In Fig., PQ ∥ AB and PR BC. IF ∠QPR = 102º, determine ∠ABC. Give reasons.

Solution 22

Question 23

Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.Solution 23

Consider the angles AOB and ACB.