Question 47

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waecmaths question: 

In the diagram$PQ\parallel TS,PR\parallel TU$ reflex angle QPS =245o, $\angle PST={{115}^{{}^\circ }},\angle STU={{65}^{{}^\circ }}$ and $\angle RPS=x$. Find the value of x

Option A: 

80o

Option B: 

70o

Option C: 

60o

Option D: 

50o

waecmaths solution: 

\[\begin{align}  & \angle SPQ=\angle PST={{115}^{\circ }}\text{   }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \angle QPR=\angle STU={{65}^{\circ }}\text{  }\!\!\{\!\!\text{ corresponding angles }\!\!\}\!\!\text{ } \\ & \angle PST+\angle PSA={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ }\angle \text{s in }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & x=\angle RPS=\angle SPQ-\angle QPR \\ & x={{115}^{\circ }}-{{65}^{\circ }}={{50}^{\circ }} \\\end{align}\]

maths year: