WAEC Mathematics 2015 Paper

Concept:Use the rule that angles on a straight line add up to $180^\circ$, then apply the alternate-angle property for parallel lines.Explanation:From the diagram, $\angle ONS = 140^\circ$.Since $M$, $N$ and $S$ lie on the same straight line, $\angle MNO$ is the supplement of $\angle ONS$.Hence,$\angle MNO = 180^\circ - 140^\circ = 40^\circ$Given $PQ \parallel RS$, the angle $\angle POM$ is the corresponding alternate angle to $\angle NMO$.Therefore,$\angle POM = 40^\circ$The value matches the straight-line angle relation and all the given conditions.Answer:$\angle POM = 40^\circ$Correct option: A. $40^\circ$