Question

the area of the shaded sector is 8π. what is the measure of ∠sot, which corresponds to the minor arc st? a 34° b 45° c 48° d 50°

Explanation:

Step1: Recall sector area formula

Sector area = $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is central angle, $r=8$.

Step2: Substitute known values

$8\pi = \frac{\theta}{360^\circ} \times \pi (8)^2$

Step3: Simplify and solve for $\theta$

Cancel $\pi$: $8 = \frac{\theta}{360^\circ} \times 64$ → $\theta = \frac{8 \times 360^\circ}{64} = 45^\circ$

Answer:

B. 45°