WAEC Mathematics 2012 Paper

Concept:The angle subtended by an arc at the centre is proportional to the length of the arc.Explanation:The total circumference is the sum of the minor and major arc lengths.$2\pi r = 54 + 126 = 180$So the radius is not needed directly because we can use the ratio of arc length to circumference.Let $\theta$ be the angle of the minor sector.$\dfrac{\theta}{360^\circ} = \dfrac{54}{180}$$\theta = \dfrac{54 \times 360^\circ}{180}$$\theta = 108^\circ$Now, angles around a point sum to $360^\circ$.Angle of the major sector $= 360^\circ - 108^\circ$$= 252^\circ$Answer:The angle of the major sector is $252^\circ$, which is option B.