Question

in the figure, angle zyx is measured in degrees. the area of the shaded sector can be determined using the formula $\frac{mangle zyx}{360^circ}(pi r^2)$.
which best explains the formula?
○ the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.
○ the central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.
○ the central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.
○ the central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.

Explanation:

The formula $\frac{m\angle ZYX}{360^\circ}(\pi r^2)$ breaks down to: the ratio of the sector's central angle ($m\angle ZYX$) to the full circle's angle ($360^\circ$), multiplied by the area of the full circle ($\pi r^2$). This matches the first option, while other options incorrectly reference circumference or skip the ratio with the full circle angle.

Answer:

The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.