I think this may be true, it works for all I’ve checked, but I’m not sure why. I stumbled across it when thinking that there must be a relation between the LCM of the interior angle and 180 degrees.
To find the number of sides of a regular polygon with interior angle x.
Odd sided polygon:
LCM(x,180)/x
Even sided polygon;
2*LCM(x,180)/x
Any ideas why, and if it always works?