Question

How do you convert $\frac{5\pi }{12}$ into degrees ?

Answer 1

With this proportion :

${\alpha }_d:{\alpha }_r={180}^{\circ }:\pi$
in which ${\alpha }_d$ is the measure of the angle in degree
and, ${\alpha }_r$ is the measure of the angle in radians.
So, if you want to convert an angle from radians in degree:

$a_d=\frac{{\alpha }_r\cdot {180}^{\circ }}{\pi }$
and if you want to convert an angle from degree to radians:
$a_r=\frac{{\alpha }_d\cdot \pi }{{180}^{\circ }}$
In our case :
$a_d=\frac{\frac{5}{4}\pi \cdot {180}^{\circ }}{\pi }={225}^{\circ }$