Question

POQ is a line.Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP andOR .prove that angle ROS=1/2(angle QOS-angle POS)?

Answer 1

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Answer 2

☺ Hello mate__ ❤

◾◾here is your answer...

Given:   OR is perpendicular to PQ

OR and OS are rays to PQ

To prove:    ∠ROS=1/2(∠QOS−∠POS)

Proof:  ∠ROQ+∠ROP=180°       (Linear pair)

⇒∠ROP=180°−∠ROQ=180°−90°=90°

R.H.S =1/2(∠QOS−∠POS)

=1/2(180°−∠POS−∠POS)                               (∠POS+∠QOS=180°)   (Linear pair)

=1/2(180°−2∠POS)          ...........eq  (1)

We have ∠POS=∠ROP−∠ROS=90°−∠ROS, putting this in eq(1), we get

R.H.S =1/2(180°−2(90°−∠ROS))

=1/2(180°−180°+2∠ROS)=1/2(2∠ROS)

=∠ROS

Therefore, L.H.S=R.H.S

Hence proved.

I hope, this will help you.

Thank you______❤

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