Poq is a line ray or is a perpendicular two line OS is another Ray lying between ray. op and or or prove that angle r o s=1\2(qos-pos)

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Solution

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)

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