Question

3
Fig. 6.17.POQ isaline. Ray OR is perpendicular
to line PO. OS is another ray lying between rays
OP and OR Prove that
ZROS== (ZQOS-ZPOS)​

Answer 1

Step-by-step explanation:

It is given that OR is perpendicular to PQ

So that ∠POR = 90°

sum of angle in linear pair always equal to 180°

∠POS + ∠SOR + ∠POR = 180°

Plug ∠POR = 90°

90°+∠SOR + ∠POR = 180°

∠SOR + ∠POR = 90°

∠ROS = 90° − ∠POS … (1)

∠QOR = 90°

Given that OS is another ray lying between rays

OP and OR so that

∠QOS − ∠ROS = 90°

∠ROS = ∠QOS − 90° … (2)

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

2 ∠ROS = ∠QOS − ∠POS

∠ROS = 1/2(∠QOS − ∠POS)