Question

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

Answer 1

It can be observed that, x + y + z + w then prove that AOB is a line.
\(⇒\)\(\text{ x+y+w+z = 360°}\)

It is given that,
\(\text{x+y = w+z}\)
So, (x + y) +(x + y) = 360°
2(x + y) = 360°
∴ (x + y) = 180° 
Since x and y form a linear pair, AOB is a line.