Question

In the fig.1.7,OP bisects angle BOC and OQ bisects angle AOC,prove that angle POQ = 90°​

Answer 1

Since OP bisects ∠ BOC.

BOC = 2(∠ POC) ...(1)

Again, OQ bisects ∠ AOC.

∠ AOC = 2(∠ QOC) ... (2)

Since ray OC stands on line AB.

∠AOC + ∠BOC = 180°

→ 2( ∠QOC) + 2( ∠POC) = 180° [Using (1)

and (2)]

→ 2(∠ POC + ∠ QOC) = 180°

⇒ ∠POC + ∠QOC = 90°

⇒ ∠POQ = 90°

Hence ∠POQ = 90° Proved.

hope it helped