Question

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

Answer 1

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