WAEC Mathematics 2018 Paper

Concept:The thread forms the complete boundary of the sector, which consists of two radii plus the curved arc.So first subtract the two radii from the total length to get the arc length, then use the arc length formula.Explanation:Total length of thread $= 21.4\,\text{cm}$.Radius of sector $= 4.2\,\text{cm}$.Two radii together $= 2 \times 4.2 = 8.4\,\text{cm}$.Arc length $= 21.4 - 8.4 = 13\,\text{cm}$.Formula for arc length is:$$L = \frac{\theta}{360^{\circ}} \times 2\pi r$$Substitute $L = 13$, $r = 4.2$, $\pi = \frac{22}{7}$:$$13 = \frac{\theta}{360^{\circ}} \times 2 \times \frac{22}{7} \times 4.2$$Multiply both sides by $360^{\circ} \times 7$:$$13 \times 360^{\circ} \times 7 = \theta \times 2 \times 22 \times 4.2$$$$13 \times 2520^{\circ} = \theta \times 184.8$$Simplify to find $\theta$:$$\theta = \frac{13 \times 2520^{\circ}}{184.8} \approx 177.27^{\circ}$$To the nearest degree, $\theta \approx 177^{\circ}$.Answer:The angle of the sector is $177^{\circ}$, so the correct option is B. $177^{\circ}$.