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(n-2)*180 =108n

180 n - 108 n = 360
72 n = 360
n = 5

drwls, I had totally misread the problem and thought it said
(n-2)^180 =108n

been working on it for almost an hour, trying Newton's method and all kinds of iteration.
I really have to try to read the questions more carefully, ha ha

You will have to use a graphical or iterative method (like Newton's) to solve that. There is no explicit closed-form answer.

(n-2)^180 =108n
If n = 3.03, you get 204 (left) & 327 (right)
If n = 3.04, you get 1164 (left) and 328 (right)
If n = 3.0326, you get 322 on the left and 327 on the right
The answer is 3.0327...

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