Reflex angles occur along with acute, right and obtuse angles, in the exterior of these angles. As the angle formed in the exterior of a straight angle is also a straight angle, reflex angle is not identified in a Straight angle.Reflex Angle Picture

Reflex angles determine the major arc in circles. It can also be viewed as the angle measured with the opposite orientation between two rays with a common end point. If an angle is denoted by ∠A, then the reflex angle is denoted by Reflex ∠A. The sum of an angle and its reflex measure is 360º.

Reflex angle is the greater angle made by two rays with a common end point, with a measure greater than 180º and less than 360º.
Reflex Angle Definition

In the above diagram the measure of angle AOB is 58º and the measure of reflex angle AOB is 360 - 58 = 302º.