The easiest way is just to count them.

However.

There are 360 degrees in a circle.

If you divide the number of sides of a polygon into that you get the value for "n"

**EXCLUDE** polygons with 0, 1 & 2 sides.

Code:

#of
sides n_value
3 120
4 90
5 72

You will notice that the angle is getting smaller with the increase in the number of sides.

When do you suppose the angle "n" will be smaller than the number of sides?

Try the square root of 360.

You will have 19 different values BUT you must exclude the "polygons" of 1 and 2 sides so you are left with 17.

There will also be 17 different values of n for a polygon of 19 sides up to a polygon of some number of sides.

Code:

360/239 = 1.506 rounds to 2
360/240 = 1.500 rounds to 2
360/241 = 1.494 rounds to 1
...
360/718 = 0.5014 rounds to 1
360/719 = 0.5007 rounds to 1
360/720 = 0.5000 rounds to 1
360/721 = 0.4993 rounds to 0

ALL polygons with sides greater that 720 will have zero for the rounded value of n.

You can create a spread sheet and determine the exact number that you are looking for very quickly.

Hope that helps.

.

Actually, the answer is provided.