Reflex Angle

An angle whose measure is greater than 180 degrees but less than 360 degrees is termed a reflex angle. An acute angle and an obtuse angle will always be shown on the other side of the reflex angle. It is less than a full rotation but more than a straight angle.

What are Reflex Angles?

A reflex angle is equal to the sum of 180 degrees and any of the primary angles such as acute angle, right angle, and obtuse angle. It is greater than a straight angle. Therefore,

• Reflex angle = 180° + Acute angle
• Reflex angle = 180° + Right angle
• Reflex angle = 180° + Obtuse angle

 

An Angle and its Reflex Angle

When two lines intersect at a point, the measure of the “opening” between these two lines is called an “Angle”. Let’s take the letters A, B, and O to name the angle.

In the above image reflex angle is the larger angle, and the smaller angle is an acute angle. It is to avoid this particular ambiguity that we refer to the angle marked outside as reflex ∠AOB.
Note: smaller ∠AOB and its reflex ∠AOB gives a sum of 360°.

Let us check one more example where two different angles can be shown together. Look at the below image showing two angles simultaneously, straight angle 180° completed at dotted green line and reflex angle 210° marked with pink circle.

In the above figures, the angle 210 degree is a reflex angle because it lies between 180° and 360°.

How to Measure a Reflex Angle?

We know that with the help of a protractor we can easily measure any type of angle. Let us look at the following ways to measure the reflex angle.

• Measure the internal angle and subtract it from 360 degrees.
• With the help of a protractor

Steps to measure a reflex angle

To measure reflex angle XYZ, follow the steps given below.

• Step 1: Place the center of the protractor at the center point and adjust it with the line that goes through 0°.

• Step 2:Now look for the point where 180 degrees completes and mark it.

• Step 3:Now measure the rest part of the angle starting from 180 degrees to the second line.

• Step 4:Once the angle beyond 180 degrees is measured, now add it to 180° to get the reflex angle that is required.

• Step 5:Now check the final measured angle, by measuring the interior angle and subtract it from 360°. This is another way to measure reflex angles and can also be effectively used for verification.