Question

In figure 6.17 POQ is a line. Ray OR is perpendicular to line PQ.O S is another ray lying between rays OP and OR. Prove that angle ROS =1/2(angle QOS - angle POS).

Answer 1

Angle QOS= angle QOR+ROS = 90 + ROS
Angle POS = POR - ROS = 90- ROS

Now,
=1/2(QOS - POS)=1/2(90+ROS+-(90-ROS)
=1/2(90+ROS-90+ROS)
cancel 90 and - 90
=1/2×2×ROS

= ROS (proved)
If correct like my answer

Answer 2

Answer:

Angle ROP = angleROQ

So we can write,

angle POS + angleROS = angleQOS -anglePOS

Here, angle POS = angleROS

So, 2(angleROS) = angleQOS - anglePOS

angle ROS = 1/2(angleQOS - anglePOS)

Hence, proved

Thank u for asking the question...bruhhh