Solving each the equations, we find that either \(x = 108\), \(x = 60\), \(x = 45\), or \(x = 72\).

The exterior angle of a regular polygon must be factor of 360, so this rules out \(x = 108\).

For the remaining three cases, \(60\)º is the exterior angle for regular hexagons, \(45\)º is for regular octagons, and \(72\)º is for regular pentagons.

Only the pentagon has a prime number of sides. Therefore, the polygon has 5 sides.