Solve 24pi=pir^2360^circ-θ/360^circ

$$24 \pi = \pi { r }^{ 2 } \frac{ 360 ^ { \circ } - \theta }{ 360 ^ { \circ } }$$

Solve for θ

$$\theta =360-\frac{8640}{r^{2}}$$

$$r\neq 0$$

Steps for Solving Linear Equation

Cancel out \pi on both sides.

$$24=r^{2}\times \frac{360-\theta }{360}$$

Multiply both sides of the equation by 360.

$$8640=r^{2}\left(360-\theta \right)$$

Use the distributive property to multiply r^{2} by 360-\theta .

$$8640=360r^{2}-r^{2}\theta$$

Swap sides so that all variable terms are on the left hand side.

$$360r^{2}-r^{2}\theta =8640$$

Subtract 360r^{2} from both sides.

$$-r^{2}\theta =8640-360r^{2}$$

The equation is in standard form.

$$\left(-r^{2}\right)\theta =8640-360r^{2}$$

Divide both sides by -r^{2}.

$$\frac{\left(-r^{2}\right)\theta }{-r^{2}}=\frac{8640-360r^{2}}{-r^{2}}$$

Dividing by -r^{2} undoes the multiplication by -r^{2}.

$$\theta =\frac{8640-360r^{2}}{-r^{2}}$$

Divide 8640-360r^{2} by -r^{2}.

$$\theta =360-\frac{8640}{r^{2}}$$

Solve for r

$$r=24\sqrt{-\frac{15}{\theta -360}}$$

$$r=-24\sqrt{-\frac{15}{\theta -360}}\text{, }\theta <360$$