Walk around any convex polygon — the total turn is 360°. So the exterior angles always sum to 360°, no matter how many sides.
Build a polygon
regular pentagon
interior each
108.0°
108.0°
exterior each
72.0°
72.0°
interior sum
540°
540°
diagonals
5
5
For a regular n-gon, each exterior angle is exactly 360°/n.