Question 41

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waecmaths question: 

The diagram is a circle with centre O. PRST are points on the circle. Find the value of $\angle PRS$

Option A: 

144o

Option B: 

72o

Option C: 

40o

Option D: 

36o

waecmaths solution: 

$\begin{align}  & \angle PRS=\tfrac{1}{2}(8x)\text{   }\!\!\{\!\!\text{ }\angle \text{ at circum =}\tfrac{1}{2}\angle \text{ at centre }\!\!\}\!\!\text{ } \\ & \angle PRS=4x \\ & \angle PRS+\angle PTS={{180}^{\circ }}\{\text{sum of opposite }\angle \text{s in a cyclic quad }\!\!\}\!\!\text{ } \\ & 4x+x={{180}^{\circ }} \\ & x={{36}^{\circ }} \\ & \angle PRS=4\times {{36}^{\circ }}={{144}^{\circ }} \\\end{align}$

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