Question

In the given figure, $\angle$RST = 56^° , seg PT $\perp$ray ST, seg PR $\perp$ ray SR and seg PR$\cong$ seg PT Find the measure of $\angle$RSP. State the reason for your answer.

Answer 1

By Part II of the angle bisector theorem, any point equidistant from sides of an angle is on the bisector of the angle
∠TSP = ∠RSP
Now, ∠TSP + ∠RSP = ∠TSR
⇒ ∠RSP + ∠RSP = 56^∘
⇒ 2∠RSP = 56^∘
⇒ ∠RSP = 28^∘
Hence, the measure of ∠RSP is 28^∘.