Question

In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = `1/2` (∠QOS − ∠POS).

Answer 1

It is given that OR ⊥ PQ

∴ ∠POR = 90°

⇒ ∠POS + ∠SOR = 90°

∠ROS = 90° − ∠POS           …(1)

∠QOR = 90°     ...(As OR ⊥ PQ)

∠QOS − ∠ROS = 90°

∠ROS = ∠QOS − 90°        …(2)

On adding equations (1) and (2), we obtain

2 ∠ROS = ∠QOS − ∠POS

∴ ∠ROS = `1/2` (∠QOS − ∠POS)