# How do you convert (5pi)/7 from radians to degree?

May 22, 2018

$128.57 \ldots$

#### Explanation:

Remember that $\pi$ radians are 180°, so you can build the following proportion, if $r$ is the angle in radians and $d$ is the angle in degree:

$r : \pi = d : 180$

From here, isolate $d$:

$d = r \cdot \frac{180}{\pi}$

So, plugging $r = \frac{5 \pi}{7}$, we have

$d = \frac{5 \cancel{\pi}}{7} \cdot \frac{180}{\cancel{\pi}} = \setminus \frac{5 \setminus \cdot 180}{7} = \setminus \frac{900}{7} = 128.57 \ldots$

May 22, 2018

It is ${900}^{\setminus \circ} / 7$
From ${\alpha}^{\setminus \circ} / \alpha = {360}^{\setminus \circ} / \left(2 \cdot \pi\right)$ we get
${\alpha}^{\setminus \circ} = {180}^{\setminus \circ} / \pi \cdot \frac{5}{7} \cdot \pi$
canceling the $\pi$ we get
${\alpha}^{\setminus \circ} = {900}^{\setminus \circ} / 7$