Question

ray os stands on the line poq. ray or and OT are angle bisectors of angle POS and angle s oq respectively if angle pos is equal to X find angle r o t.



ANS PLZ

Answer 1

hope this helps you , dear

Answer 2

Answer:

$\angle ROT=90^{\circ}$

Step-by-step explanation:

We are given that

Ray OS stands on the line POQ.

$\angle POS=x$

We have to find the angle ROT.

We are given that ray OR and OT are angle bisector of angle POS and angle SOQ.

$\angle POR=\angle ROS$

$\angle SOT=\angle TOQ$

$\angle POS+\angle SOQ=180^{\circ}$ (by linear pair sum)

$x+\angle SOQ=180^{\circ}$

$\angle SOQ=180-x$

$\angle POR+\angle ROS=x$

$\angle POR+\angle POR=x$

$2\angle POR=x$

$\angle POR=\frac{x}{2}$

$\angle POR=\angle ROS=\frac{x}{2}$

$\angle SOT+\angle TOQ=\angle SOQ=180-x$

$\angle SOT+\angle SOT=180-x$

$2\angle SOT=180-x$

$\angle SOT=\frac{180-x}{2}=90-\frac{x}{2}$

$\angle ROT=\angle ROS+\angle SOT=\frac{x}{2}+90-\frac{x}{2}$

$\angle ROT=90^{\circ}$