What are Reflex Angles?
Different types of angles are used in geometry for spatial measurements. An angle that has a measure between 180° and 360° is known as a reflex angle.
There is always a corresponding angle on the other side of a reflex angle. This corresponding angle can either be an acute angle, an obtuse angle, or even a right angle.
Together, a reflex angle and the corresponding angle on the other side of it add up to 360°. For example, take a look at the reflex angle image. This reflex angle measures 312° and the acute angle corresponding to it measures 48°.
312° + 48° = 360°
How to Find the Measure of a Reflex Angle?
Now that we know the sum of a reflex angle and its corresponding angle add up to 360°, the measure of the reflex angle can be calculated by subtracting the corresponding internal angle from 360°. So to find the reflex angle, first we need to determine the internal angle with the help of a protractor. Let’s see how to measure a reflex angle by following these steps:
Step 1: Using a protractor, measure the internal angle. Let’s consider the internal angle here measures 120° .
Step 2: Now, we subtract the value of the internal angle from 360° to get the corresponding reflex angle, that is 360° – 120° = 240°.
Step 3: As a result, we can see the reflex angle measures 240°, as shown in the image.
Rapid Recall
Solved Reflex Angle Examples
Example 1:
Ron ordered a pizza that has been cut into 6 equal slices. After eating two slices of pizza what would be the angle of the remaining slices?
Solution:
As we know, the shape of a pizza is usually a full circle. So the angle = 360°.
It is mentioned that the pizza slices are equally sliced into 6 pieces. So, let’s divide the angle of a full pizza by the number of slices, that is = 360° \(\div\) 6 = 60°
The angle of each slice = 60°
Since, Ron has eaten two slices of pizza, the angle of two slices would be 120°
To find the angle of the remaining slices, let’s subtract the angle of two slices from 360°, that is, 360° – 120° = 240°
The angle of the remaining pizza slices is 240°, which is a reflex angle.
Example 2:
Find the corresponding reflex angle of 70°.
Solution:
Given internal angle = 70°
As we already know, to find the reflex angle we need to subtract the internal angle from 360°
Then, 360° – 70° = 290°
Hence, the corresponding reflex angle of 70° is 290°.
Example 3:
If the interior angle of the letter ‘V’ is 50°, find the measure of its reflex angle.
Solution:
Given, the interior angle of the letter ‘V’ = 50°
So, to find the exterior reflex angle of the letter ‘V’, we should subtract the interior angle from 360°.
Then,
Reflex angle = 360 °- 50°
= 310°
So, the exterior angle of the letter ‘V’ is 310°.
As we all know, a reflex angle is greater than 180 degrees. On the other hand the sum of all internal angles of a triangle equals 180 degrees. So, it’s not possible to draw a reflex angle triangle. Though it is possible to create a triangle, using the interior angle of the reflex angle.
The protractor is a tool that is used to measure and draw different angles.
Measuring angles can improve spatial knowledge and the link between numbers and measurements.
No, 180 degree is not a reflex angle. It is a straight angle. Reflex angles always measure between 180 degree and 360 degree.
Yes, a concave quadrilateral can have a reflex angle, but a convex quadrilateral cannot. It is because all the angles in a convex quadrilateral are less than 180° and concave quadrilaterals have one angle that is greater than 180°.