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.
The full angle around a point is 360º. Hence as seen in the definition of the reflex angle, the reflex measure of an angle is got by subtracting the angle measure from 360º.

Examples:
Find the reflex measure of angles given.
The angle measure is given as 74º.
The reflex angle measure = 360 - 74
= 286º.
Solving Reflex Angle
The given angle is a right angle.
The Reflex measure of a right angle
= 360 - 90
= 270º

How to Solve Reflex Angle
The angle measure is given as 144º.
The reflex angle measure
= 360 - 144
= 216º.
Calculating Reflex Angle

The reflex angle measure in all the three above examples is between 180 and 360 degrees. Thus an angle and its reflex angle make the full angle around the vertex of the angle.
The measure of an interior angle of a regular hexagon is 120º. This makes the reflex angle at a vertex of a regular hexagon to be equal to = 360 -120 = 240º.

Hexagon Reflex Angle

This means the measure of the reflex angle is twice the measure of the interior angle for a regular hexagon. The dotted line shown in the diagram is the bisector of the reflex angle at a vertex. The reflex angle is thus divided into two equal angles of measure 120º.

This property makes it possible to tessellate regular hexagons. That means congruent hexagons can be tiled around a vertex to make new designs as shown below.

Hexagon Tesselation

The other similar polygons that are used in tessellations are equilateral triangles and squares. The measure of an angle of an equilateral triangle is 60º. Hence the measure of the reflex angle at the vertex is 300º, which is a multiple of 60.

Similarly, each angle in a square is a right angle, and the reflex angle measures 270º, which is a multiple of 90º, which makes it possible to tessellate with squares.