The area of a sector of a circle is given by the equation $A=\frac{\pi r^{2} S}{360}$, where $r$ is the radius of the circle and $S$ is the angle measure of the sector. If Mia solved this equation for $S$, which of the following equations did she write?
$360 A+\pi r^{2}$
$360 A-\pi r^{2}$
$\frac{360+A}{\pi \pi^{2}}$
$\frac{360 A}{\pi r^{2}}$

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