In the diagram O is the centre of the circle $\overline{RT}$is a diameter, $\angle POT={{33}^{\circ }}$ and $\angle TOS={{76}^{\circ }}$. Use the diagram to answer question 19 and 20
20. Find the size of angle PRS
76o
71o
38o
33o
$\begin{align} & \left| OT \right|=\left| OS \right|\text{ }\!\!\{\!\!\text{ Radius of a circle }\!\!\}\!\!\text{ } \\ & \angle OTS=\angle OST\text{ }\!\!\{\!\!\text{ Base }\angle s\text{ of Iss }\vartriangle \} \\ & \text{Consider }\vartriangle OTS \\ & \angle TOS+\angle OTS+\angle OST={{180}^{\circ }} \\ & {{76}^{\circ }}+a+a={{180}^{\circ }} \\ & a={{52}^{\circ }} \\ & \angle OTS=\angle OST={{52}^{\circ }} \\ & \text{Also }\angle TSR={{90}^{\circ }}\text{ }\!\!\{\!\!\text{ Angle in a semi circle }\!\!\}\!\!\text{ } \\ & \angle TRS+\angle RTS+\angle TSR={{180}^{\circ }} \\ & \angle TRS+{{52}^{\circ }}+{{90}^{\circ }}={{180}^{\circ }} \\ & \angle TRS={{38}^{\circ }} \\ & \angle PRS=\angle TRS+\angle PRT={{38}^{\circ }}+{{33}^{\circ }}={{71}^{\circ }} \\\end{align}$