Answer
$\frac{180^{\circ}}{\pi}$
Work Step by Step
Using the circumference of a circle given by the formula $C=2\pi r$ and remembering that $\pi$ radians has a measure of a $180^{\circ}$ angle, we solve $180^{\circ}=\pi$ $radians$ for angles and for radians.
Solving for degrees,
$180^{\circ}=\pi$ $radians$
Dividing both sides by $180^{\circ}$.
$\frac{180^{\circ}}{180}=\frac{\pi radians}{180}$
$1^{\circ}=\frac{\pi}{180}$ $radians$
Solving for radians,
$180^{\circ}=\pi$ $radians$
Dividing both sides by $\pi$.
$\frac{180^{\circ}}{\pi}=\frac{\pi radians}{\pi}$
$1 radian=\frac{180^{\circ}}{\pi}$
To convert to degrees, multiply a radian measure by $\frac{180^{\circ}}{\pi}$ and simplify.
