What is the maximum number of sides a regular polygon can have such that its interior angles (in degrees) are integers?

Question

The ratio between the exterior angle and the interior angle of a regular polygon is 2 : 3 .
Find the number of sides of the polygon.

Answer 1

By definition, the interior angles of a regular polygon must be less than 180°, maximizing the interior angles also maximizes the number of sides. The largest integer less than 180 is 179, and an interior angle of 179° would mean an exterior angle of 180°-179°=1°, and n=360°/1°=360 sides.