Question:
In 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 = \(\frac{1}{2}\) (\(∠\)QOS – \(∠\)POS)
In 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 = \(\frac{1}{2}\) (\(∠\)QOS – \(∠\)POS)
Updated On: Jan 20, 2026
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Solution and Explanation
It is given that (OR ⊥ PQ) and \(∠\)POQ = 180°
We can rewrite it as \(∠\)ROP = \(∠\)ROQ = 900
Since, \(∠\)ROP =\(∠\)ROQ
It can be written as
\(∠\)POS + \(∠\)ROS = \(∠\)ROQ
\(∠\)POS + \(∠\)ROS = \(∠\)QOS – \(∠\)ROS
\(∠\)SOR + \(∠\)ROS = \(∠\)QOS – \(∠\)POS
\(⇒\) 2\(∠\)ROS = \(∠\)QOS – \(∠\)POS
i.e, \(∠\)ROS = \(\frac{1}{2}\) (\(∠\)QOS – \(∠\)POS)
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