Answer :

Suppose that

BOC = 2x and ∠ AOC = 2y

Now, by question; OP and OQ is the bisect or of ∠ BOC and ∠ AOC respectively.

⇒

Similarly,

Now,

∠ POQ = ∠ POC + ∠ COQ = x + y

So, we have to find ∠ POQ i.e.x + y Now, ∠ BOC + ∠ AOC = 180

⇒ 2x + 2y = 180

⇒ 2(x + y) = 180

⇒ x + y = 180/2

⇒ x + y = 90°

Hence, ∠ POQ = 90°.

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