+199 We first go by the exterior angle measure: \(\frac{360}{n}\).
Now, \(n\) has to be a factor of \(360\) , so we count how many factors this number has.
Since \(360=2^3*3^2*5\)\(\) , we add one to each power, resulting in \(4*3*2=24\) factors.
Finally, a polygon cannot have one or two sides; thus the answer is \(24-2=\boxed{22}\) regular polygons.
+199 We first go by the exterior angle measure: \(\frac{360}{n}\).
Now, \(n\) has to be a factor of \(360\) , so we count how many factors this number has.
Since \(360=2^3*3^2*5\)\(\) , we add one to each power, resulting in \(4*3*2=24\) factors.
Finally, a polygon cannot have one or two sides; thus the answer is \(24-2=\boxed{22}\) regular polygons.
