WAEC Mathematics 2016 Paper

Concept:Opposite angles of a cyclic quadrilateral are supplementary, and the tangent-chord theorem relates the tangent angle to the angle in the alternate segment.Explanation:From the diagram, $PQRS$ is a cyclic quadrilateral and $\angle PQR = 117^\circ$.Opposite angles of a cyclic quadrilateral add up to $180^\circ$.So, $\angle PSR = 180^\circ - 117^\circ = 63^\circ$.In $\triangle PRS$, $|PR|=|SR|$, so it is isosceles.Thus, the base angles are equal:$\angle PSR = \angle RPS = 63^\circ$.Using the angle sum of a triangle,$63^\circ + 63^\circ + \angle PRS = 180^\circ$.Therefore, $\angle PRS = 180^\circ - 126^\circ = 54^\circ$.By the tangent-chord theorem, the angle between tangent $ST$ and chord $SP$ equals the angle in the alternate segment.Hence, $\angle PST = \angle PRS = 54^\circ$.Answer:$54^\circ$ (Option A).