A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

An acute angle is the smallest angle measuring between 0 to 90 degrees, whereas the obtuse angle measures between 90 and 180 degrees. The right angle is exactly equal to 90 degrees.

Apart from these, there are three other types such as straight, reflex and full rotation. A straight angle is equal to 180 degrees and full rotation is equal to 360 degrees. Full rotation is also termed a full circle. Let us learn here how an angle is said to be a reflex.

Reflex Angle Definition

As we have already discussed in the introduction, the reflex angle is the angle greater than 180 degrees and less than 360 degrees.

A reflex angle is equal to the sum of 180 degrees and any of the primary angles (acute, right and obtuse angles). Therefore,

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

Degree

As per the definition of reflex angle, any degree which lies between a straight angle (180°) and full rotation (360°) is a reflex angle. Hence, 181°, 190°, 200°, 210°, 220°, 230°, 240°, 250°, 260°, 270°, 280°, 290°, 300°, 310°, 320°, 330°, 340°, 350°, 359°, are all reflex angles.

Reflex Angle Diagram

In the figure given below, the angle is a reflex angle that lies between 180° and 360°.

Reflex angle Triangle

As we know, the measurement of a reflex angle is greater than 180 degrees, whereas the sum of all internal angles is equal to 180 degrees. Thus, it is not possible to draw a reflex angle triangle.

How to measure a reflex angle?

There are two ways to measure the reflex angle.

• By measuring the interior angle and subtracting it from 360 degrees.
• By using a protractor to measure the reflex angle itself

Steps to measure a reflex angle:

Since the measure of a reflex angle is greater than 180 degrees and the protractor has the maximum measure of 180 degrees, therefore we need to follow the below steps to measure the reflex angle.

1. Place the center of the protractor above the center point where the two lines of the angle lie and make sure the line goes through 0°.
2. Now mark with the point where 180 degrees completes.
3. Now we need to measure the rest of the angle from 180 degrees to the given second line.
4. After measuring the angle beyond 180 degrees, we need to add it to 180° to get the required reflex angle.
5. You can check the resultant angle, by measuring the interior angle and subtracting it from 360°.

Reflex Angle Examples

We can observe many reflex angles in our daily existence. For example, the hands of a clock form reflex angle at 7’O clock, 8’O clock, and so on when we measure in the clockwise direction. Also, we can identify this type of angle when we attempt to separate slices from pizza.

Solved Problems

Question 1:

What is the reflex angle of 110 degrees?

Solution:

To find the reflex angle of a given angle, we need to subtract the given measure from 360 degrees.

So, the reflex angle of 110 degrees = 360 – 110 = 250.

Therefore, the reflex angle of 110 degrees is equal to 250 degrees.

Question 2:

Find the reflex angle of 60 degrees?

Solution:

To find the reflex angle of a given angle, we need to subtract the given measure from 360 degrees.

So, the reflex angle of 60 degrees = 360 – 60 = 300.

Therefore, the reflex angle of 60 degrees is equal to 300 degrees.

Worksheet

Draw a reflex angle for the given measurements:

• 190°
• 270°
• 370°
• 345°
• 241°