To solve the given equation for the angle measure [tex]\( S \)[/tex] of the sector, we start with the equation for the area [tex]\( A \)[/tex] of a sector of a circle:
[tex]\[ A = \frac{\pi r^2 S}{360} \][/tex]
We need to isolate [tex]\( S \)[/tex] on one side of the equation. Here is the step-by-step process:
1. Multiply both sides by 360:
[tex]\[ 360A = \pi r^2 S \][/tex]
2. Divide both sides by [tex]\( \pi r^2 \)[/tex]:
[tex]\[ S = \frac{360 A}{\pi r^2} \][/tex]
Thus, the resulting equation, which expresses [tex]\( S \)[/tex] in terms of [tex]\( A \)[/tex] and [tex]\( r \)[/tex], is:
[tex]\[ S = \frac{360 A}{\pi r^2} \][/tex]
Therefore, the correct equation Mia wrote is:
[tex]\[ \boxed{\frac{360 A}{\pi r^2}} \][/tex]
