JAMB Mathematics 2014 Paper

Concept:Use the properties of parallel lines, angle bisectors, and the angle sum of a triangle.Explanation:Since $KL \parallel NM$, the alternate interior angles formed by transversal $LN$ are equal.So, $\angle KLN = \angle LNM = 54^\circ$.Given that $LN$ bisects $\angle KNM$, it divides that angle into two equal parts:$\angle KNL = \angle LNM = 54^\circ$.Therefore, $\angle KNM = \angle KNL + \angle LNM = 54^\circ + 54^\circ = 108^\circ$.Now consider $\triangle KMN$.The sum of its interior angles is $180^\circ$:$\angle MKN + \angle KMN + \angle KNM = 180^\circ$.Substitute the known values:$35^\circ + \angle KMN + 108^\circ = 180^\circ$.So, $\angle KMN = 180^\circ - 143^\circ = 37^\circ$.Answer:$\angle KMN = 37^\circ$, so the correct option is C.