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∘, find ∠ROT.
Ray OS stands on the line POQ so that,
∠POS+∠SOQ=180∘
But, ∠POS=x
Hence, x+∠SOQ=180∘
∠SOQ=180∘–x
Now, ray OR bisects ∠POS.
Hence, ∠ROS=12×∠POS=12×x=x2
Similarly, ∠SOT=12×∠SOQ=12×(180∘−x)=90∘–x2
∠ROT=∠ROS+∠SOT=x2+90∘–x2=90∘