Angles are measured in either degrees or in radians. Radians are preferred more than degrees for pure mathematics.
           A degree is a measure of angle which is subtended by an arc that is
$\frac{1}{360}$ full rotation,is said to have measure of one degree($1^{\circ}$) that is equivalent to $\frac{\pi}{180}$ radians. The degree is represented by degree symbol $^{\circ}$.
A radian is also an angular measurement unit. Radian measurement is equal to length of the arc. Radian of subtended angle is the ratio of length of arc of the circle to the radius of the circle.
                                      $\theta = \frac{a}{r}$
   where $\theta$ is the angle subtended, a is the arc length and r is radius.
Converting from Radians to Degrees:
To convert from radian to degree,multiply by $\frac{180}{\pi}$

degrees = radians $\times$ $\frac{180^{\circ}}{\pi}$

Converting from Degrees to Radians:
To convert from degree to radian,multiply by $\frac{\pi}{180}$

radians = degrees $\times$ $\frac{\pi}{180^{\circ}}$