Question

In figure, ray OS stands on a line POQ. Ray OR and ray OT are angle bisector
bf angle POS and angle SOQ respectively. If angle POS = x, find angle ROT.​

Answer 1

Given, angle POS= x

Then, angle POR=angle ROS=x/2

Now, let angle SOQ= y/2

Then,angle SOT= angle TOQ=y/2

Here, POQ is straight line.

So, angle POR+angle ROS+angle SOT+ angle TOQ=180°

x/2+x/2+y/2+y/2=180

x+y=180°

Dividing both sides by 2...

x/2+y/2=180/2

angle ROS+ angle SOT=90°

or, angle ROT=90°