Question

in figure 6.17 is a line. ray OR is perpendicular to line PQ. OS is another ray lying between ray OP and OR. prove angle ROS=1/2(angle QOS - angle POS)

Answer 1

Let angle Ros be x
according to question pos= 90-x and qos= 90+x
x=1/2[90+x-(90-x)]
x= 1/2(2x)
x=x
rhs=lhs
hence proved

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✿❁═══┅✿