Question

2 &
w
c)) In the figure alongside, if x + y + z = 180°,
prove that w = y + z.​

Answer 1

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.

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.

Hope this will help you....