180(n-2)/n degrees, or 180-360/n.
There is another way to see this is so. Imagine walking around the
perimeter of the n-gon. Observe that at each corner of angle x
degrees we must turn ourselves 180-x degrees to remain on the
perimeter. And after traversing the entire perimeter we should have
turned a total of 360 degrees.
Thus, setting n(180-x)=360 we get x= (180n-360)/n, which is the same
as our previous calculation.
Thus we know exactly what regular n-gons look like.
What shapes in 3 space are analogous to polygons?
to find out!
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