WAEC Mathematics 2017 Paper

Concept:Use the angle in a semicircle and the tangent-chord theorem.Explanation:Since $RPS$ is a diameter, the angle subtended at $S$ is $\angle RSP = 90^\circ$.In $\triangle RSP$,$\angle RPS = 180^\circ - (90^\circ + 24^\circ) = 66^\circ$.Because $RP$ is produced to $T$, $R$, $P$ and $T$ are collinear.Therefore, $\angle TPS = 180^\circ - \angle RPS = 180^\circ - 66^\circ = 114^\circ$.By the tangent-chord theorem, the angle between tangent $TS$ and chord $SP$ equals the angle in the alternate segment:$\angle TSP = \angle SRP = 24^\circ$.In $\triangle TPS$, since $TR$ and $TP$ lie on the same line,$\angle STR = \angle PTS = 180^\circ - (114^\circ + 24^\circ) = 42^\circ$.Thus, the required angle is $42^\circ$.Answer:B. $42^\circ$