WAEC Mathematics 2018 Paper

Concept:Equal chords subtend equal central angles at the centre of a circle. Also, radii of the same circle are equal, forming isosceles triangles.Explanation:Since O is the midpoint of WZ, O is the centre of the semicircle, and WZ is a diameter.Therefore, $\angle WOZ = 180^{\circ}$.Given $|WX| = |XY| = |YZ|$, the corresponding central angles are equal:$\angle WOX = \angle XOY = \angle YOZ$.So, $\angle YOZ = \frac{180^{\circ}}{3} = 60^{\circ}$.In $\triangle YOZ$, $OY = OZ$ because both are radii.Hence, the base angles are equal: $\angle OYZ = \angle OZY = m$.Using the angle sum of a triangle:$60^{\circ} + m + m = 180^{\circ}$$2m = 120^{\circ}$$m = 60^{\circ}$.Answer:B. $60^{\circ}$