Question

Please answer this Friends . send me reply as photo

Answer 1

. 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

∠ROS = 1

2 (∠QOS – ∠ POS)

Sol. ∠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