Question

"Question 4 In the given figure, if x+y=w+z , then prove that AOB is a line.

Class 9 - Math - Lines and Angles Page 97"

Answer 1

given=x+y=w+z
=>we can say( w+z= x+y)
=>(x+y)+(x+y)=360. (complete angle)
=>2(x+y) =360
=>x+y =180.

Hence sum of angle of straight line is 180
=>AOB is a straight line.

Answer 2

A.67

 

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

 

Axiom- 1

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.

 

Axiom-2

If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.

 

The two axioms given above together are called the linear pair axioms.

 

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Solution:

 

Given,
x + y = w + z

To Prove,

AOB is a line or

x + y = 180° (linear pair.)

Proof:

A.T.Q

x + y + w + z = 360° (Angles around a point.)

(x + y) +  (w + z) = 360°

(x + y) +  (x + y) = 360°

(Given x + y = w + z)

2(x + y) = 360°

(x + y) = 180°

Hence, x + y makes a linear pair.

Therefore, AOB is a straight line.

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Hope this will help you....