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Question

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


A

180

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B

90

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C

120

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D

75

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Solution

The correct option is B

90


Ray OS stands on the line POQ, so,

POS+SOQ=180 {Linear pair}

Given, POS=x.

Hence ,x+SOQ=180

SOQ=180x.

Now, ray OR bisects POS.

Hence, ROS=12×POS
12×x=x2.

Similarly, SOT=12×SOQ
12×(180x)=90x2

Hence , ROT=ROS+SOT
x2+90x2=90.


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