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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