WAEC Mathematics 2023 Paper

Concept:Use the angle-at-the-centre theorem and the property of an isosceles triangle formed by two radii.Explanation:$\angle SQR = 28^{\circ}$ is an inscribed angle subtending arc $SR$.The central angle $\angle SOR$ subtending the same arc is twice the inscribed angle.So, $\angle SOR = 2 \times 28^{\circ} = 56^{\circ}$.In $\triangle SOR$, $OS = OR$, since both are radii of the circle.Therefore, $\triangle SOR$ is isosceles, and the base angles are equal.Thus, $\angle ORS = \angle OSR$.The sum of angles in $\triangle SOR$ is $180^{\circ}$.So, $\angle ORS = \frac{180^{\circ} - 56^{\circ}}{2} = \frac{124^{\circ}}{2} = 62^{\circ}$.Answer:$\angle ORS = 62^{\circ}$, which is option D.