Question 22

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waecmaths question: 

In the diagram $MQ\parallel RS,\angle TUV={{70}^{\circ }}\text{and }\angle RLV={{30}^{\circ }}$ find the value of x

Option A: 

150o

Option B: 

110o

Option C: 

100o

Option D: 

95o

waecmaths solution: 

$\begin{align}  & \angle RBD={{30}^{\circ }} \\ & \angle MAB=\angle RBD={{30}^{\circ }}\text{ }\!\!\{\!\!\text{ corresponding }\angle \text{s }\!\!\}\!\!\text{ } \\ & \angle EAC=\angle MAB={{30}^{\circ }}\text{ }\!\!\{\!\!\text{ Vertically opp }\angle \text{s }\!\!\}\!\!\text{ } \\ & \angle AEC+\angle EAC=\angle ACT\text{  }\!\!\{\!\!\text{ sum of opp two }\angle \text{s }\!\!\}\!\!\text{ } \\ & x=\angle ACT={{70}^{\circ }}+{{30}^{\circ }}={{100}^{\circ }} \\\end{align}$

maths year: