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= }(<QOS – ZPOS
o
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∠ROS=90∘−∠POS−(i)
∠QOS=∠QOR+∠ROS=90∘+∠ROS
⇒90∘=∠QOS−∠ROS−(ii)
Substituting (ii) in (i) we get
∠ROS=∠QOS−∠ROS−∠POS
⇒2∠ROS=∠QOS−∠POS
⇒∠ROS=21(∠QOS−∠POS)
Hence proved.
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