Reflex Angle: Diagram & Examples

In geometry, reflex angle is a type of angle that is greater than 180 degrees and less than 360 degrees. There are various types of angles like acute angle, obtuse angle, right angle and straight angle.

• Each angle is related to the other because if you explain an acute angle, you will say an angle that is less than a right angle (90 degrees).
• An obtuse angle is an angle that is more than 90 degrees but less than 180 degrees.
• It has a corresponding angle, which lies on the other side of the angle.
• These angles are used in the field of trigonometry and physics. 
• Any angle, like a 200-degree angle, 230-degree angle, etc, is a reflex angle because these angles are greater than 180 degrees.

Key Terms: Reflex angle, Acute angle, Obtuse angle, Straight angle, Right angle, Internal angle, Angles, Circle, Geometry, Reflex Angle Diagram

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Reflex Angle Definition

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As you have seen in the introductory part, the reflex angle is an angle that is greater than 180 and less than 360 degrees. It means this angle will always be greater than a half-circle (180 degrees) and less than a full circle (360 degrees).

• It will form a complete angle of 360 degrees with a corresponding angle that lies on the other side.
• The first part of the angle will be either acute, obtuse, or right angles. 
• To every obtuse and acute angle, there is a reflex angle. 
• Let x be an acute or obtuse angle, and k is the reflex angle, then:

x+k = 360 and k=360-x

• It means we can easily compute the reflex angle if the value of the acute or obtuse angle is given.
• It can be written like this:

Reflex angle = 180° + Acute angle

Reflex angle = 180° + Right angle

Reflex angle = 180° + Obtuse angle

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How to measure a Reflex Angle?

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There are two simple methods of measurement of reflex angle by which you can easily find out this angle:

• By using a protractor, you can measure the reflex angle
• By finding the internal angle and subtracting it from 360 degrees

Steps to measure a Reflex Angle

The steps to measure a reflex angle are as follows:

Step 1

First, calculate the internal angle by using a protector. It would help if you used a protector in the manner where the lines meet, which means in the center. Then, measure the internal angle to point to the protector. 

• The internal angle in this figure is 110 degrees, angle XYZ = 110 degrees.

Step 2

By measuring the internal angle, which is 110 degrees, subtract this value from 360 degrees to find the reflex angle. It can be written like this.

• 360 degrees - 110 degrees = 250 degrees

Step3

So, the reflex angle can be calculated by using the protector in this figure; the reflex angle is 250 degrees.

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Degree

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An angle refers to the measurement of the space between two intersecting lines. The sum of the reflex angle and its corresponding angle is 360 degrees, which can easily calculate the degrees of a reflex angle. 

• The exterior angle is equivalent to the sum of the two corresponding obtuse or acute angles.
• The reflex angle rotates in a clockwise direction along the vertex.
• In this diagram, the angle is shown as greater than 180 degrees and less than 360 degrees.
• As we know, the full circle is 360 degrees, and the half-circle is 180 degrees. 
• So, the reflex angle must lie between 180 degrees and 360 degrees. 

Reflex Angle Diagram

Hence these all angles are 181°, 190°, 200°, 210°, 220°, 230°, 240°, 250°, 260°, 270°, 280°, 290°, 300°, 310°, 320°, 330°, 340°, 350°, 359°, are all reflex angles.

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Reflex Angle Examples in Real Life

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There are many examples of reflex angles in our day-to-day life which are as follows:

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Things to Remember

• An angle that is greater than 180 degrees is a half-circle, and less than 360 degrees is a full circle.
• The reflex angle can be found by adding acute angle, right angle, and obtuse angle in 180 degrees.
• The best way to calculate these angles is by using a protector.
• More than half the revolution of a clock is also a reflex angle
• The exterior angle of a polygon is the sum of the two remote interior angles. 

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