Question

In the given figure , POQ is a straight line. OR⊥ PQ. OS lies between OP and OR .Prove that ∠ ROS = ½ (∠ QOS - ∠ POS )

Answer 1

I HOPE IT WILL BE HELPFUL TO YOU.

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______❤

✿┅═══❁✿ Be Brainly✿❁═══┅✿