POQ is a line ray OR is a perpendicular to line PQ. OS is another ray lying between ray OP and OR. Prove that ∠ROS=12(∠QOS−∠POS)
Given:- OR⊥PQ
To prove:-
∠ROS=12(∠QOS−∠POS)
Proof:-
∵OR⊥PQ
∴∠ROP=90°
∠ROQ=90°
∴ We can say that,
∠ROP=∠ROQ
∠POS+∠ROS=∠ROQ[∵∠ROP=∠POS+∠ROS]
⇒∠POS+∠ROS=∠QOS−∠ROS[∵∠ROQ=∠QOS−∠ROS]
⇒∠ROS+∠ROS=∠QOS−∠POS
⇒2∠ROS=∠QOS−∠POS
⇒∠ROS=12(∠QOS−∠POS)