Question 3

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waecmaths question: 

In the diagram $\angle PSR={{22}^{{}^\circ }},\text{ }\angle SPQ={{58}^{{}^\circ }}$ and Calculate the obtuse angle QRS

Option A: 

99o

Option B: 

100o

Option C: 

121o

Option D: 

165o

waecmaths solution: 

\[\begin{align}  & \text{Produce line }QR\text{ to line }SP\text{ to meet at point }B \\ & \angle PBQ+\angle BPQ+\angle BQP={{180}^{\circ }}\text{  }\!\!\{\!\!\text{ }\angle \text{s in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle PBQ+{{58}^{\circ }}+{{41}^{\circ }}={{180}^{\circ }} \\ & \angle PBQ={{81}^{\circ }} \\ & \angle SBR={{180}^{\circ }}-\angle PBQ={{180}^{\circ }}-{{81}^{\circ }}={{99}^{\circ }} \\ & \angle QRS=\angle SBR+\angle BSR\text{  } \\ & \text{ }\!\!\{\!\!\text{ sum of two opposite angle of a triangle }\!\!\}\!\!\text{ } \\ & \angle QRS={{99}^{\circ }}+{{22}^{\circ }}={{121}^{\circ }} \\\end{align}\]

maths year: