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

We know that,

Sum of all angles round a point is equal to 360°.

⇒ x + y + w + z = 360°

⇒ (x + y) + (w + z) = 360°

As,

x + y = w + z

⇒ (x + y) + (x + y) = 360°

⇒ 2(x + y) = 360°

⇒ (x + y) = $\dfrac{360°}{2}$ = 180°.

⇒ x + y = 180° and w + z = 180°.

Since the sum of adjacent angles, x and y with OA and OB as the non-common arms is 180° we can say that AOB is a straight line.

Hence, proved that AOB is a straight line.