Explanation

A regular n-gon has exterior angle 360/n, so the angle must divide 360. Here 360/4 = 90, 360/5 = 72, 360/6 = 60, 360/8 = 45 - all integers. Hence all four can be exterior angles. Forgetting that n need not be small (n = 90 for 4 degrees) is the trap.