Question 37

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waecmaths question: 

In the diagram, STUV is a straight line$\angle TSY=\angle UXY={{40}^{{}^\circ }}$ and $\angle VUW={{110}^{\circ }}$ calculate $\angle TYW$

Option A: 

150o

Option B: 

140o

Option C: 

130

Option D: 

120o

waecmaths solution: 

$\begin{align}  & \angle WUS={{180}^{\circ }}-\angle VUW={{180}^{\circ }}-{{110}^{\circ }}={{70}^{\circ }} \\ & \text{ }\!\!\{\!\!\text{ sum of }\angle s\text{ on a straight line }\!\!\}\!\!\text{ } \\ & \angle SWU={{180}^{\circ }}-\angle WUS-\angle WSU\text{  }\!\!\{\!\!\text{ }\angle s\text{ in a }\vartriangle \} \\ & \angle SWU={{180}^{\circ }}-{{40}^{\circ }}-{{70}^{\circ }}={{70}^{\circ }} \\ & \angle XYW=\angle SWU-\angle YXW\text{ } \\ & \text{ }\!\!\{\!\!\text{ sum of two opp}\text{. }\angle s\text{ in }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle XYW={{70}^{\circ }}-{{40}^{\circ }}={{30}^{\circ }} \\ & \angle XYW+\angle TYW={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ sum of }\angle s\text{ on a st}\text{. line }\!\!\}\!\!\text{ } \\ & \angle TYW={{180}^{\circ }}-{{30}^{\circ }}={{150}^{\circ }} \\\end{align}$

maths year: