Question 46

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waecmaths question: 

In the diagram $\angle WOX={{60}^{\circ }}$, $\angle YOE={{50}^{\circ }}$and $\angle OXY={{30}^{\circ }}$what is the bearing of X from Y

Option A: 

300o

Option B: 

240o

Option C: 

190o

Option D: 

150

waecmaths solution: 

\[\begin{align}  & \angle XOY={{180}^{\circ }}-\angle WOX-\angle EOY\text{ } \\ & \text{ }\!\!\{\!\!\text{ }\angle \text{s on a str}\text{. line }\!\!\}\!\!\text{ } \\ & \angle XOY={{180}^{\circ }}-{{50}^{\circ }}-{{60}^{\circ }}={{70}^{\circ }} \\ & \angle OYX={{180}^{\circ }}-\angle XOY-\angle OXY \\ & \angle OYX={{180}^{\circ }}-{{70}^{\circ }}-{{30}^{\circ }}={{80}^{\circ }} \\ & \angle NOY={{90}^{\circ }}-\angle YOE={{90}^{\circ }}-{{50}^{\circ }}={{40}^{\circ }}\text{ } \\ & \text{ }\!\!\{\!\!\text{ right angle }\!\!\}\!\!\text{ } \\ & \angle OYA=\angle NOY={{40}^{\circ }}\text{  }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & \text{The bearing of X from Y}={{180}^{\circ }}+{{40}^{\circ }}+{{80}^{\circ }} \\ & \text{The bearing of X from Y}={{300}^{\circ }} \\\end{align}\]

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