How do you convert $\frac{5 π}{7}$ $(5pi)/7$ from radians to degree?

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Answer 1 · 2018-05-22T10:08:04

$128.57...$

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 $d$ :

$d = r*180/pi$

So, plugging $r=(5pi)/7$ , we have

$d = (5cancel(pi))/7*180/cancel(pi) = \frac{5\cdot 180}{7} = \frac{900}{7} = 128.57...$

Answer 2 · 2018-05-22T10:11:19

It is $900^{\circ}/7$

From $alpha^{\circ}/alpha=360^{\circ}/(2*pi)$ we get
$alpha^{\circ}=180^{\circ}/pi*5/7*pi$
canceling the $pi$ we get
$alpha^{\circ}=900^{\circ}/7$

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