WAEC Mathematics 2018 Paper

Concept:Use parallel-line angle properties and the alternate segment theorem for a tangent to a circle.Explanation:Since $QT \parallel RS$ and $SQ$ is a transversal, alternate interior angles are equal:$\angle TQS = \angle RSQ = 50^\circ$.The points $P$, $Q$, and $R$ lie on the same straight tangent line, so the angles at $Q$ on that line add up to $180^\circ$:$\angle PQT + \angle TQS + \angle SQR = 180^\circ$.Substitute the known values:$\angle PQT + 50^\circ + 35^\circ = 180^\circ$$\angle PQT = 180^\circ - 85^\circ = 95^\circ$.By the alternate segment theorem, the angle between tangent $QP$ and chord $QT$ is equal to the angle subtended by chord $QT$ at point $S$:$\angle QST = \angle PQT = 95^\circ$.Answer:$95^\circ$ (Option D).