WAEC Mathematics 2013 Paper

Concept:A regular pentagon has equal exterior angles, and extending two sides forms a triangle whose base angles are these exterior angles.Explanation:The polygon $PQRST$ has 5 sides, so $n = 5$.Each exterior angle of a regular pentagon is$$\text{exterior angle} = \frac{360^\circ}{5} = 72^\circ.$$When $QR$ and $TS$ are produced to meet at $V$, triangle $RVS$ is formed.At $R$, the angle between $RV$ and $RS$ is the exterior angle, so $\angle VRS = 72^\circ$.At $S$, the angle between $RS$ and $SV$ is also the exterior angle, so $\angle RSV = 72^\circ$.In $\triangle RVS$,$$\angle RVS = 180^\circ - (72^\circ + 72^\circ)$$$$\angle RVS = 180^\circ - 144^\circ = 36^\circ.$$Answer:$36^\circ$, which is option A.