WAEC Mathematics 2019 Paper

Concept:The angle subtended at the centre by an arc is found using the relation between arc length, radius, and angle.Explanation:The formula for the length of an arc is:$$L = \frac{\theta}{360^\circ} \times 2\pi r$$Here, $L = 22$ cm and $r = 15$ cm.Substitute the given values and $\pi = \frac{22}{7}$:$$22 = \frac{\theta}{360^\circ} \times 2 \times \frac{22}{7} \times 15$$Simplify the right-hand side:$$22 = \frac{\theta}{360^\circ} \times \frac{660}{7}$$Rearrange to solve for $\theta$:$$\theta = \frac{22 \times 360^\circ \times 7}{660}$$$$\theta = \frac{22 \times 360^\circ \times 7}{2 \times 22 \times 15}$$Cancel the common factor of $22$:$$\theta = \frac{360^\circ \times 7}{30}$$$$\theta = 84^\circ$$Thus, the angle subtended at the centre is $84^\circ$.Answer:$84^{\circ}$Option B.