WAEC Mathematics 2010 Paper

Concept:Angles on a straight line add up to $180^\circ$, and equal radii form an isosceles triangle.Explanation:Since $POQ$ is a straight line, the adjacent angles at $O$ are supplementary.From the diagram, $\angle POR = 56^\circ$.Therefore, $\angle POR + \angle QOR = 180^\circ$.So, $56^\circ + \angle QOR = 180^\circ$.$\angle QOR = 180^\circ - 56^\circ = 124^\circ$.Now, $OQ$ and $OR$ are radii of the circle, so $OQ = OR$.Hence, $\triangle QOR$ is isosceles.Thus, the base angles are equal:$\angle OQR = \angle ORQ = 2x$.Using the angle sum of a triangle:$2x + 124^\circ + 2x = 180^\circ$$4x + 124^\circ = 180^\circ$$4x = 180^\circ - 124^\circ = 56^\circ$$x = \frac{56^\circ}{4} = 14^\circ$.Answer:$x = 14^\circ$Therefore, the correct option is D.