In the diagram, RP is a diameter of the circle RSP, RP is produced to T and TS is a tangent to the circle at S. If $\angle PRS={{24}^{\circ }}$, Calculate the value of $\angle STR$
24o
42o
48o
66o
$\begin{align} & \angle RSP=90{}^\circ \text{ }\!\!\{\!\!\text{ Angle subtended in a semicircle }\!\!\}\!\!\text{ } \\ & \angle PST=\angle SRP={{24}^{\circ }}\text{ }\!\!\{\!\!\text{ Alternate segments }\!\!\}\!\!\text{ } \\ & \angle SPT=\angle SRP+\angle RSP\text{ }\!\!\{\!\!\text{ Sum of opp}\text{. interior }\angle \text{s }=\text{opp ext angle }\!\!\}\!\!\text{ } \\ & \angle SPT=24{}^\circ +90{}^\circ =114{}^\circ \\ & \text{Consider }\vartriangle SPT \\ & \angle PST+\angle SPT+\angle STP=180{}^\circ \text{ }\!\!\{\!\!\text{ Sum of }\angle \text{s in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & 24{}^\circ +114{}^\circ +\angle STP=180{}^\circ \\ & \angle STP=180{}^\circ -138{}^\circ =42{}^\circ \\\end{align}$