In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ respectively. Find ∠ROT.
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Solution
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Ray OS stands on the line PQ.
Therefore, ∠POS+∠SOQ=1800 (Linear pair)
Let ∠SOQ=x0
Thus ∠POS=1800−∠SOQ
∠POS=1800−x0
Now, ass ray OR and ray OT are angle bisectors so
∠SOT=12×∠SOQ
Thus, ∠SOT=12×x0
And ∠ROS=12×∠POS
Thus, ∠ROS=12×(1800−x0)
∠ROS=900−x02
Here ∠ROT=∠ROS+∠SOT
∠ROT=900−x02+x02
∠ROT=900.
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