Question

In fig.5.26,if x+y=w+z,then prove that AOB is a line.​

Answer 1

Answer:

As Given, x+y=w+z

To Prove: AOB is a line or x+y=180

(linear pair.)

According to the question,

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.

Answer 2

Answer:

It can be observed that,

x + y + z + W = 360°. (complete angle)

It is given that,

x + y = z + W

.: x + y + x + y = 360°

2(x + y) = 360°

x + y = 180°

Since x and y form a linear pair, AOB is a line.