Some might argue than reflex angles are not real. They are the 'other half' of a smaller angle. Indeed if you refer to the angle ∠ABC without qualifying it,it is generally assumed that you mean the smallest angle. If you mean the large part of the angle, you must specify it by saying 'reflex angle ∠ABC'.
Altogether, there are six types of angle as listed below. Click on an image for a full description of that type and a corresponding interactive applet.
Less than 90°
Between 90° and 180°
Between 180° and 360°