RD SHARMA Solutions for Class 9 Maths Chapter 10 - Lines and Angles

Chapter 10 - Lines and Angles Exercise 10.51

Question 1

One angle is equal to three times its supplement. The measure of the angle is

(a) 130°

(b) 135°

(c) 90°

(d) 120°

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 7

In figure, the value of y is

(a) 20°

(b) 30°

(c) 45°

(d) 60°

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Chapter 10 - Lines and Angles Exercise 10.52

Question 1

In figure, the value of x is

(a) 12

(b) 15

(c) 20

(d) 30

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

In figure, which of the following statements must be true?

(i) a + b = d + c     (ii)  a + c + e = 180°          (ii)  b + f = c + e

(a) (i) only

(b) (ii) only

(c) (iii) only

(d) (ii) and (iii) only

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Chapter 10 - Lines and Angles Exercise 10.53

Question 1

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the measure of the larger angle is

(a) 54°

(b) 120°

(c) 108° 

(d) 136°

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Chapter 10 - Lines and Angles Exercise 10.54

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Chapter 10 - Lines and Angles Exercise 10.55

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

In figure, if lines l and m are parallel, then x = 

(a) 20°

(b) 45°

(c) 65°

(d) 85°

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Chapter 10 - Lines and Angles Exercise 10.56

Question 1

In figure, if lines l and m are parallel lines, then x = 

(a) 70°

(b) 100°

(c) 40°

(d) 30°

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

In figure, if lines l and m are parallel, then the value of x is

(a) 35°

(b) 55°

(c) 65°

(d) 75°

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is

(a) 45°

(b) 30°

(c) 36°

(d) none of these

Solution 4

Correct option (c)

Let one angle be θ

Then, its complementary = 90 - θ

According to question,

2θ = 3(90 - θ)

5θ = 270

θ = 54°

Then,  90 - θ° = 36°

Hence, the smaller angle is 36°.

Hence, correct option is (c).

Chapter 10 - Lines and Angles Exercise 10.57

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

In figure, if line segment AB is parallel to the line segment CD, What is the value of y?

(a) 12

(b) 15

(c) 18

(d) 20


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Chapter 10 - Lines and Angles Exercise Ex. 10.1

Question 1

Write the complement of each of the following angles:

(i) 20o

(ii) 35o

(iii) 90o

(iv) 77o

(v) 30o

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

Write the supplement of each of the following angles:

(i) 54o

(ii) 132o

(iii) 138o

Solution 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 28o less than its complement, find its measure.

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

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

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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 xo.

Its complement will be (90o - xo) and its supplement will be (180o - xo).

Supplement of thrice of the angle = (180o - 3xo)

According to the given information:

(90o - xo) = (180o - 3xo)

3x - x = 180 - 90

2x = 90

x = 45

Thus, the measure of the angle is 45o.

The measure of the angle is 45o

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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?

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 2

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

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

Question 4

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

 

 

 

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

Solution 4

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 5

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 7

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 8

In fig., determine the value of x.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 9

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 10

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 11

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 12

Give Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And AnglesPOR = 3x and Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And AnglesQOR = 2x + 10, find the value of x for which POQ will be aline.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 13

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 16

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

 

 

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 17

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 19
In 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
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
                                    Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Solution 19
Given that OR ⊥ PQ  
 
 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And AnglesPOR = 90o   
 
    ⇒ POS  + SOR = 90o
 
ROS = 90 - POS                ... (1)
 
    QOR = 90o                     (As OR ⊥ PQ) 
 
   QOS - ROS = 90o
 
    ROS = QOS - 90o             ... (2)
 
    On adding equations (1) and (2), we have
 
    2 ROS = QOS - POS
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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.

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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.

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

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

 



Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

In Fig., find the value of X.

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 6

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

(i) Determine y when x = 60o

(ii) Determine x when y = 40

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 7

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 9

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

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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 90o.

(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 90o.

Solution 10

(i) True

(ii) False

(iii) False

(iv) True

Question 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 180o, then the ______ arms of the two angles are opposite rays.

Solution 11

(i) obtuse.

(ii) 180o

(iii) uncommon

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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.

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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.

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

 

 

 

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 3

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 4

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 5

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 6

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 7

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

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Let AB and CD be perpendicuar to line MN.


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Question 10

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

 

 

 


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 11

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


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Let AB and CD be perpendicuar to line MN.


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Question 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 15

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

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 16

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

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 17

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

 
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 21

In fig., show that AB  EF.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 22

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

 

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

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.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 24

In fig.,  lines AB and CD are parallel and p is any point as shown in the figure. Show that ABP + CDP = DPB.

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Solution 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 25

In fig., AB ∥ CD and P is any point shown in the figure. Prove that:

ABP + BPD + CDP = 360°

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Solution 25

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 26

In fig., arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC = ∠DEF

 

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles 
Solution 26

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 



Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Question 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

 

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles
Solution 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Lines And Angles