WAEC Mathematics 2010 Paper

Concept:The angle subtended by an arc at the centre is twice the angle subtended at the circumference. Angles in the same segment of a circle are equal.Explanation:In the circle, $\angle SQR$ and $\angle SPR$ stand on the same chord $SR$. Since $\angle SQR = 60^\circ$, the angle in the same segment $\angle SPR$ is also $60^\circ$. So $y = 60^\circ$. The central angle $\angle SOR$ subtends the same arc $SR$ as $\angle SQR$. Therefore, $\angle SOR = 2 \times \angle SQR$. That is, $3x = 2 \times 60^\circ = 120^\circ$. So $x = \frac{120^\circ}{3} = 40^\circ$. Now add the two values: $x + y = 40^\circ + 60^\circ = 100^\circ$.Answer:$100^\circ$ Option B.