Question 18

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waecmaths question: 

In the diagram $\overline{YW}$is a tangent to the circle at X, $\left| UV \right|=\left| VX \right|$and $\angle VXW={{50}^{\circ }}$, find the value of $\angle UXY$ 

Option A: 

70o

Option B: 

80o

Option C: 

105o

Option D: 

110o

waecmaths solution: 

$\begin{align}  & \angle XUW=\angle VXW={{50}^{\circ }}\text{    }\!\!\{\!\!\text{ }\angle \text{s in alternate segments }\!\!\}\!\!\text{ } \\ & \angle UXW=\angle XUW={{50}^{\circ }}\text{    }\!\!\{\!\!\text{ Base }\angle \text{s of Isso }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle VXW+\angle UXV+\angle YXU={{180}^{\circ }}^{\circ }\text{   }\!\!\{\!\!\text{ Sum of }\angle s\text{ in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \text{5}{{\text{0}}^{\circ }}+\text{5}{{\text{0}}^{\circ }}+\angle YXU={{180}^{\circ }} \\ & \angle YXU={{80}^{\circ }} \\\end{align}$

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