Question

Three Marks
6. Ray OC stands on the line AB. Ray Or bitects BOC and ray OP hinta Lase,

Prove that ZPOR = 90'.​

Answer 1

We are given that, ray OR bisects ∠BOC and ray OP bisects ∠AOC. We have to prove that ∠POR = 90°.

Here,

∠BOC + ∠AOC = 180° [Linear Pair]

⟹ 2∠POC + 2∠ROC = 180°

[Since the angles are bisected]

⟹ 2(∠POC + ∠ROC) = 180°

⟹ 2(∠POR) = 180°

⟹ ∠POR = 180°/2

∴ ∠POR = 90°.

Hence, Proved.