Reflex angle – Definition – Examples

Reflex angle

Based on the measurements, angles are classified into 5 types

1. Acute angle (0° < θ < 90°)
2. Right angle (θ = 90°)
3. Obtuse angle (90° < θ < 180°)
4. Straight angle (θ = 180°)
5. Reflex angle (180° < θ < 360°)
6. Complete angle (θ = 360°)

If the measure of the angle is greater than that of a straight angle (180°) but smaller than that of a complete angle (360°), it is called a reflex angle.

Since the reflex angle is always greater than 180° but less than 360°, we can write it as the sum of straight angles and other angles which are less than a straight angle.

1. Straight angle + Acute angle 
2. Straight angle + Right angle 
3. Straight angle + Obtuse angle

It can be also written in the following forms

1. Complete angle – acute angle 
2. Complete angle – right angle 
3. Complete angle – obtuse angle

Measurement using protractors

An angle less than 180° can be easily measured through a protractor. For angles more than 180°, we can’t measure it directly using protractors. Here we have to measure the smaller angle using the protractor and then subtract it from 360°.

Here is an example showing the procedure.

Example

Find the measure of the reflex angle ∠AOB

1. We have to find the measure larger angle ∠b and it is greater than 180°. It is not possible to measure it using a protractor because a protractor can only measure up to 180°.
2. But angle ∠a is less than 180° and we can measure that. The measure of ∠a = 140° is shown in the figure and it is an obtuse angle.
3. We already know that 

Reflex angle = Complete angle – obtuse angle

                       = 360° – 140°

                       = 220°

4. Hence the measure of ∠AOB = ∠b is 220°.