WAEC Mathematics 2012 Paper

Concept:Bearings are measured clockwise from the north direction. North lines are parallel, so alternate angles can be used to connect the given bearing to the angle at $Q$.Explanation:Let $QB$ be the south direction from $Q$.Since the north line at $P$ is parallel to the line through $Q$, the alternate angle gives$\angle PQB = \angle NPQ = 50^\circ$.From the diagram, $R$ lies on the other side of $QB$ from $P$.Given $\angle PQR = 72^\circ$, the angle between $QR$ and $QB$ is$72^\circ - 50^\circ = 22^\circ$.Since $QB$ is the south direction, the bearing from the north direction to $R$ is$180^\circ - 22^\circ = 158^\circ$.Answer:The bearing of $R$ from $Q$ is $158^\circ$.Correct option: C. $158^\circ$.