JAMB Mathematics 2016 Paper

Concept:Use properties of parallel lines, alternate angles, and the angle sum on a straight line.Explanation:Since $l_1 \parallel l_2$, the transversal creates alternate angles that are equal.At point $P$, angles on a straight line add to $180^\circ$, so $\angle MPT = 180^\circ - 118^\circ = 62^\circ$.Therefore, $\angle PML = 62^\circ$ because it is the alternate angle to $\angle MPT$.At point $M$, the angles $y$, $2y + 10^\circ$, and $62^\circ$ lie on a straight line, so:$y + (2y + 10^\circ) + 62^\circ = 180^\circ$$3y + 72^\circ = 180^\circ$$3y = 108^\circ$$y = 36^\circ$Thus, $\angle PMT = 2y + 10^\circ = 2(36^\circ) + 10^\circ = 82^\circ$.Answer:The value of $\angle PMT$ is $82^\circ$, which corresponds to option A.