JAMB 2014 · UTME · Q26

In the figure, $KL \parallel NM$ and $LN$ bisects $\angle KNM$ . If $\angle KLN = 54^\circ$ and $\angle MKN = 35^\circ$ , calculate $\angle KMN$ .

Worked solution (try it first)

$KL \parallel NM$ , so $\angle LNM = \angle KLN = 54^\circ$ (alternate angles).
$LN$ bisects $\angle KNM$ , so $\angle KNM = 2 \times 54^\circ$
$= 108^\circ$ .
The angles of triangle $KMN$ add up to $180^\circ$ : $\angle KMN = 180^\circ - 108^\circ - 35^\circ$
$= 37^\circ$ , option D.