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If you name the degree of the angle d, then the exterior angle is 180 - d. The exterior angles have to add up to 360, a full circle to get back to where you started. So if there are nsides and n angles,

n(180-d) = 360

Solving for d, you get

180 n - nd = 360

-nd = 360 - 180n

-d = 360/n - 180

and then

d = 180 - 360/n

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