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Question

In the figure, ray OS stand on a line POQ. Ray OR and ray OT are angle bisectors of POS and SOQ respectively. If POS=x, find ROT

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Solution

Ray OR stands on a line POQ forming POS and QOS


OR and OT the angle bisects of POS and QOS respectively. POS=x
But POS+QOS=180 (Linear pair)
x+QOS=180QOS=180x
OR and OT are the bisectors of angle
ROS=x2
and TOS=180x2
ROT=ROS+TOS=x2+180x2=x+180x2=1802=90


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