WAEC Mathematics 2019 Paper

Concept:The angle between a tangent and a chord drawn at the point of contact equals the angle in the alternate segment of the circle.Explanation:From the diagram, $RT$ is a tangent to the circle at $R$, and $RQ$ is a chord.The angle between the tangent $RT$ and the chord $RQ$ is given as $\angle QRT = 52^\circ$.Let the angle subtended by chord $RQ$ at point $S$ on the alternate arc be $\angle QSR$.By the alternate segment theorem, $\angle QRT = \angle QSR$.The diagram marks $\angle QSR = y$.Therefore, $y = 52^\circ$.The other given angles are not needed for finding $y$.Answer:$y = 52^\circ$Correct option: C. $52^\circ$