waecmaths question:
In the diagram, $MN\parallel PO,$ $\angle PMN={{112}^{{}^\circ }},\angle PNO={{129}^{{}^\circ }}\angle NOP={{37}^{{}^\circ }}$ and$\angle MPN=y$ find the value of y
Option A:
51o
Option B:
54o
Option C:
56o
Option D:
66o
waecmaths solution:
\[\begin{align} & \angle OPN={{180}^{\circ }}-({{129}^{\circ }}+{{37}^{\circ }})={{14}^{\circ }}\text{ }\!\!\{\!\!\text{ }\angle \text{s in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle PNM=\angle OPN={{14}^{\circ }}\text{ }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \angle MPN={{180}^{\circ }}-(\angle PNM+\angle PMN)\text{ }\!\!\{\!\!\text{ }\angle \text{s in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & y=\angle MPN={{180}^{\circ }}-({{112}^{\circ }}+{{14}^{\circ }})={{54}^{\circ }} \\\end{align}\]
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