Question

In the figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that 

Answer 1

∠ROS = ∠ROP – ∠POS …(1) 

and ∠ROS = ∠QOS – ∠QOR …(2) 

Adding (1) and (2), 

∠ROS + ∠ROS = ∠QOS – ∠QOR 

+ ∠ROP – ∠POS 

⇒ 2∠ROS = ∠QOS – ∠POS (∵ ∠QOR = ∠ROP = 90°) 

⇒ ∠ROS = 1 2 (∠QOS – ∠POS) Proved.