Question 24

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Jambmaths question: 

In the diagram above, $\angle RPS={{50}^{o}}$, $\angle RPQ={{30}^{o}}$and PQ = QR . Find the value of $\angle PRS$

Option A: 

50o

Option B: 

60o

Option C: 

70o

Option D: 

80o

Jamb Maths Solution: 

$\begin{align}  & \angle QPR=\angle QRP={{30}^{o}}\text{     }\!\!\{\!\!\text{ Base angle of issosceles }\Delta \text{ }\!\!\}\!\!\text{ } \\ & \angle PQR+{{30}^{o}}+{{30}^{o}}={{180}^{o}}\text{   }\!\!\{\!\!\text{ Sum of }\angle \text{s in }\Delta PQR\} \\ & \angle PQR+\angle PSR={{180}^{o}}\text{    }\!\!\{\!\!\text{ sum of opp}\text{.}\angle \text{s in a cyclic quad }\!\!\}\!\!\text{ } \\ & \angle PSR={{180}^{o}}-{{120}^{o}}={{60}^{o}} \\ & \angle PSR+\angle PRS+\angle RPS=180\text{    }\!\!\{\!\!\text{ Sum of }\angle \text{s in }\Delta PSR\} \\ & {{60}^{o}}+\angle PRS+{{50}^{o}}={{180}^{o}} \\ & \angle PRS={{70}^{o}} \\\end{align}$

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