Question

POQ is a line. ray OR is perpendicular to line PQ. OS is another ray lying between Rays OP and OR.

Answer 1

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.

Answer 2

Step-by-step explanation:

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