Question 26

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Jambmaths question: 

In the figure above, $KL\parallel NM$, LN bisect $\angle KNM$. If angle KLN is 54o and angle MKN is 35o. Calculate the size of angle

Option A: 

37o

Option B: 

19o

Option C: 

91o

Option D: 

89o

Jamb Maths Solution: 

$\begin{align}  & \angle LNM=\angle KLN={{54}^{\circ }}\text{     }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & \angle KNM=2\times \angle LNM\text{  }\!\!\{\!\!\text{ }LN\text{ bisect }\angle KNM \\ & \angle KNM=2\times {{54}^{\circ }}={{108}^{\circ }} \\ & \angle MKN+\angle KNM+\angle KMN={{180}^{\circ }}\text{  }\!\!\{\!\!\text{ Sum of }\angle s\text{ in a }\Delta \text{ }\!\!\}\!\!\text{ } \\ & \text{3}{{\text{5}}^{\circ }}+{{108}^{\circ }}+\angle KMN={{180}^{\circ }} \\ & \angle KMN={{37}^{\circ }} \\\end{align}$

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