POQ is a line. ray OR is perpendicular to line PQ. OS is another ray lying between Rays OP and OR.
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Note : I am assuming this as your question : In the given 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= 1/2 ( ∠QOS-∠POS)
Answer:
Take ∠SOQ
⇒∠SOQ = ∠QOR + ∠ROS
⇒∠SOQ = 90 + ∠ROS
⇒∠SOQ -∠ROS = 90
Next , take ∠POR
∠POR = ∠POS+∠ROS
90 = ∠POS+∠ROS
Now , equate them
∠SOQ - ∠ROS = ∠POS +∠ROS
Take∠ ROS to one side
2∠ROS = ∠POS-∠SOQ
Hence ,
∠ROS = 1/2(∠QOS-∠POS)
Hence , it has been proved.
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