WAEC Mathematics 2012 Paper

Concept:In a circle, the angle at the centre is twice the angle at the circumference standing on the same arc. Also, angles around a point sum to $360^\circ$.Explanation:From the diagram, the two angles formed at the centre of the circle are $2x$ and $8x$.Together they make one complete turn about the centre.Therefore, $2x + 8x = 360^\circ$.So, $10x = 360^\circ$, which gives $x = 36^\circ$.The required angle $\angle PRS$ is an angle at the circumference.It stands on the same arc as the larger central angle $8x$.Hence, $\angle PRS = \frac{1}{2} \times 8x$.$\angle PRS = 4x = 4 \times 36^\circ = 144^\circ$.Answer:$144^\circ$Correct option: A.