Answer
See below.
Work Step by Step
When observing the central angle of a sector of a circle with radius r, we also observe the portion of the circumference (s) subtended by the central angle.
We can express the angle in degrees, where a full circle angle has $360^{o}$.
We can also express the angle as the ratio $\displaystyle \theta=\frac{s}{r}$.
This is called the radian measure of the angle.
A full circle has circumference $s=2\pi r$, so the radian measure corresponding to $360^{o}$ is $2\pi.$
From here, we see that $\pi$ radians is equivalent to $180^{o}.$
Conversion formulas are obtained from the proportion:
( radian measure of an angle) to $\pi$ = (angle measure in degrees) to $180^{o}$
or
$\displaystyle \frac{\theta}{\pi}=\dfrac{\alpha}{180^{o}}\quad \Rightarrow\left\{\begin{array}{l}
\theta=\dfrac{\alpha\cdot\pi}{180^{o}}\\
\\
\alpha=\dfrac{\theta\cdot 180^{o}}{\pi}
\end{array}\right.$
where $\theta$= measure in radians, $\alpha$ = measure in angle degrees.
