An angle will separate the plane into three sets. First you have the points which lie on the two lines that make up the angle. Then you have points which lie on the either side of the angle (since the two rays which make the angle divides the plane into two parts).
For the second part I don't quite understand what you mean by the exterior. For polygons there are interior and exterior angles but for an angle itself what is meant by interior and exterior? The vertex is the intersection point of the rays that make up the angle.