Even in a non-simple polygon, it may be possible to define the exterior angle. Still, one will have to pick an orientation of the plane (or surface) to decide the sign of the exterior angle measure. In Euclidean geometry, the sum of the exterior angles of a simple convex polygon, if only one of the two exterior angles is assumed at each vertex, will be one full turn (360°).
The concept of an exterior angle applies to polygons regardless of their complexity. The sign of the exterior angle depends on the chosen orientation of the plane or surface. In Euclidean geometry, the sum of exterior angles for a simple convex polygon is always 360 degrees.