Question

If ray OC stands on line AB such that ∠AOC = ∠COB, then show that ∠AOC = 90°.

Answer 1

Since ray OC stands on line AB. 

Therefore

∠AOC + ∠COB = 180° (Linear pair of angles)

But ∠AOC = ∠COB (given)

⇒ 2∠AOC = 180°

⇒ ∠AOC = 90°