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Question
In the below fig, POQ is a line. Ray OR is perpendicular to line OS is another ray lying
between rays OP and OR. Prove that ∠ROS = 1 (∠QOS − ∠POS).
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Solution
Given that, OR perpendicular
∴`∠`POR = 90°
`∠`POS + `∠`SOR = 90° [∴ `∠`POR = `∠`POS + `∠`SOR]
`∠`ROS = 90° - `∠`POS ..........(1)
`∠`QOR = 90° (∴ OR ⊥ PQ)
`∠`QOS - `∠`ROS = 90°
`∠`ROS = `∠`QOS - 90° .........(2)
By adding (1) and (2) equations, we get
2`∠`ROS = `∠`QOS - `∠`POS
`∠`ROS = `1/2` (`∠`QOS - `∠`POS )
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