JAMB Mathematics 2020 Paper

Concept:The equal sides create isosceles triangles, so their base angles are equal. Then use the straight line and quadrilateral angle sum.Explanation:Because $PQ = PR$, in $\triangle PQR$, the base angles are equal:$\angle PQR = \angle QRP = y$.Because $PR = PS$, in $\triangle PRS$, the base angles are equal:$\angle PRS = \angle RSP = x$.Therefore, the interior angle at $R$ of quadrilateral $PQRS$ is:$\angle QRS = \angle QRP + \angle PRS = y + x$.Since $Q$, $R$, and $T$ lie on a straight line, the angles at $R$ are supplementary:$\angle QRS + \angle SRT = 180^\circ$$y + x + 68^\circ = 180^\circ$$x + y = 180^\circ - 68^\circ = 112^\circ$.Now apply the angle sum of quadrilateral $PQRS$:$\angle QPS + y + (y + x) + x = 360^\circ$$\angle QPS + 2(x + y) = 360^\circ$$\angle QPS = 360^\circ - 2(112^\circ)$$\angle QPS = 360^\circ - 224^\circ = 136^\circ$.Answer:$\angle QPS = 136^\circ$The correct option is A.