Question 20

loading...

Prev/Next links

waecmaths question: 

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

Option A: 

76o

Option B: 

71o

Option C: 

38o

Option D: 

33o

waecmaths solution: 

$\begin{align}  & \left| OT \right|=\left| OS \right|\text{    }\!\!\{\!\!\text{ Radius of a circle }\!\!\}\!\!\text{ } \\ & \angle OTS=\angle OST\text{    }\!\!\{\!\!\text{  Base }\angle s\text{ of Iss }\vartriangle \} \\ & \text{Consider }\vartriangle OTS \\ & \angle TOS+\angle OTS+\angle OST={{180}^{\circ }} \\ & {{76}^{\circ }}+a+a={{180}^{\circ }} \\ & a={{52}^{\circ }} \\ & \angle OTS=\angle OST={{52}^{\circ }} \\ & \text{Also }\angle TSR={{90}^{\circ }}\text{   }\!\!\{\!\!\text{ Angle in a semi circle }\!\!\}\!\!\text{ } \\ & \angle TRS+\angle RTS+\angle TSR={{180}^{\circ }} \\ & \angle TRS+{{52}^{\circ }}+{{90}^{\circ }}={{180}^{\circ }} \\ & \angle TRS={{38}^{\circ }} \\ & \angle PRS=\angle TRS+\angle PRT={{38}^{\circ }}+{{33}^{\circ }}={{71}^{\circ }} \\\end{align}$

maths year: 
maths topics: