Question

If AB I a line,OP bisects Z BOC and OQ bisects
Z AOC,then find Z POQ.​

Answer 1

Solution:-

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.