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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