Question 21

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waecmaths question: 

In the diagram P, Q, R, S are points on the circle $R\overset{\wedge }{\mathop{Q}}\,S$ = 30o, $P\overset{\wedge }{\mathop{R}}\,S$ = 50o and $P\overset{\wedge }{\mathop{S}}\,Q$ = 20o. What is the value of xo + yo ?

Option A: 

260o

Option B: 

130o

Option C: 

100o

Option D: 

80o

waecmaths solution: 

$\begin{align}  & \angle SPR=\angle SQR=30\text{    }\!\!\{\!\!\text{ }\angle s\text{ in the same segment }\!\!\}\!\!\text{ } \\ & \text{Consider }\vartriangle PSR \\ & \angle SPR+\angle PSR+\angle SRP={{180}^{\circ }} \\ & {{30}^{\circ }}+{{(20+x)}^{\circ }}+{{50}^{\circ }}={{180}^{\circ }} \\ & x={{80}^{\circ }} \\ & \text{Consider }\vartriangle SRZ \\ & \angle ZSR+\angle SRZ+\angle SZR={{180}^{\circ }} \\ & \angle SZY={{50}^{\circ }} \\ & y=\angle PZY=\angle SZY={{50}^{\circ }}\text{  vertically opposites }\angle s\} \\ & x+y={{50}^{\circ }}+{{80}^{\circ }}={{130}^{\circ }} \\\end{align}$

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