Question

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

Answer 1

Given seg PT $\perp$ ray ST
seg PR $\perp$ ray SR
seg PR $\cong$ seg PT
Any point equidistant from sides of an angle is on the bisector of the angle.
P is a point on the bisector of TSR.
$\angle RST={56}^{\circ }$ [Given]
$\angle RSP=\frac{1}{2}\angle$RST [Bisector of an angle divides it into two equal angles]
$\angle$RSP =$\frac{1}{2}\times {56}^{\circ }={28}^{\circ }$
Hence measure of $\angle RSPis{28}^{\circ }$.