A reflex angle is an angle that measures greater than 180° but less than 360°.
It is larger than a straight angle but does not form a full circle.
∠WQY is a reflex angle.
Look at the angles below. Which is a reflex angle?
∠CAT is a reflex angle.
Finding Reflex Angles in the Real World
Reflex angles can be tricky to find because they are the larger part of an angle’s opening. One way to think about them is as the “exterior” or “larger counterpart” of an acute, right, or obtuse angle.
The interior of a clock’s hands at 6:10 forms an acute angle, but the larger exterior angle is a reflex angle.
A laptop opened to a 90° angle forms a right angle between the screen and keyboard, but the larger exterior angle on the other side is a reflex angle.
A stop sign forms obtuse angles where its sides meet, but the larger exterior angles around the sign are reflex angles.
Since reflex angles measure greater than 180° but less than 360°, they are always the larger opening of a two-ray formation.
Can you find any reflex angles around you?
Measuring a Reflex Angle with a Protractor
Most protractors measure only up to 180°, so how do we measure a reflex angle?
To measure a reflex angle, follow these steps:
- Measure the smaller interior angle (the acute, right, or obtuse angle inside).
- Subtract that measurement from 360° to find the reflex angle.
For example, if an interior angle measures 50°, the reflex angle is: 360° – 50° = 310°.
If you have a full-circle (360°) protractor, you can measure reflex angles in one step!
The protractor shows a reflex angle of 210°, while the smaller interior angle is 150°.
Together, these two angles complete a full 360° circle.
210° + 150° = 360°
When you add the interior angle and its reflex counterpart, they always sum to 360°, forming a complete circle!
Practice Problems
Which is a reflex angle?
Which of the following is a reflex angle?
If an interior angle measures 135°, what is its reflex angle?
360° – 135° = 225°
A straight angle is a type of reflex angle.
A straight angle is exactly 180°, and a reflex angle must be greater than 180° but less than 360°.
