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I used the equation i=180 (n-2)/n, where i is the internal angle of the polygon and n is the number of the sides of the polygon.

After some trials, i got to the answer. The regular polygon with greater number of sides has n=360 sides and internal angle i = 179 degrees. The answer of the question is that there are 24 polygons with the needed conditions (you need to factorize 360 = 2³ 3² 5 and make the permutations of the exponents, that are 4 (0,1,2,3), and 3 and 2, then you have the total number of divisors of 360).

The interesting thing, I thought today, is that there are 360 sides, this means that when this polygon is limited by a circumference you find that 2 consecutive vertices connected to the center had a 1 degree angle between the lines that connect them. So it appears to me that this is the origin of the degree scale in angles, the polygon with greatest number of sides that have an integer internal angle.

Someone confirms my thesis??