Question

POQ is a line. ray OR is perpendicular to line PQ.OS is another ray lying between rays OP and OR. prove that angel ROS=1/2 (angel qos-angel POS)

Answer 1

We have , ROS + POS = 90° and , POS + QOS = 180 °

:- POS + QOS = 2( ROS + POS )

2 ROS = QOS - POS. → ROS = 1/2 ( QOS - POS )

Answer 2

Hey !!

Here is your answer...

Given :- OR perpendicular to PQ.
So, angle POR = 90°

angle POS + angle SOR + angle POR = 180
... ( Sum of angle of linear pair is 180° )

90 + angle POS + angle SOR = 180

angle SOR = 90 - angle POS ----- ( 1 )

angle QOR = 90°
As given that OS is ray lying between OP and OR.
angle QOS - angle SOR = 90

angle SOR = angle QOS - 90 ------ ( 2 )

Comparing eq. ( 1 ) and eq. ( 2 ) we get,
2 angle SOR = angle QOS - angle POS

angle SOR = 1/2 ( angle QOS - angle POS )..proved

THANKS ^-^