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. |
90∘
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∘