Reflex Angle

A reflex angle is an angle that is greater than 180 degrees but less than 360 degrees. A reflex angle always has a corresponding angle which lies on the other side of it. Let us learn more about reflex angles in this article.

A reflex angle is an angle that lies between 180° and 360°. A reflex angle and the corresponding angle that lies on the other side of it together form a complete angle of 360°. Observe the following figure to see what a reflex angle looks like.

Reflex Angle Definition

A reflex angle is always greater than a straight angle which is a half-circle (180°), and less than a complete angle which is a full circle (360°). It should be noted that a reflex angle always has an acute angle, an obtuse angle, or a right angle on the other side of it.

We know that a reflex angle and its corresponding angle add up to 360°. Therefore, the degrees of a reflex angle can be easily calculated. For example, if an acute angle measures 56°, then its corresponding reflex angle will be 360° - 56° = 304°. Similarly, if an obtuse angle measures 97°, then its corresponding reflex angle will be 360° - 97° = 263°.

When two lines intersect at a point, the measure of the “opening” between these two lines is called an angle. Let us take the letters A, B, and O to name the angle. Observe the following figure to see the reflex angle which 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: Reflex ∠AOB and the acute ∠AOB form a complete angle, therefore, they sum up to 360°.

We know that with the help of a protractor we can easily measure any type of angle. Let us learn how to measure a reflex angle using the following steps. Observe the following figure to relate to the steps.

• Step 1: Measure the internal angle with the help of a protractor. Here, we measure the internal angle as 110°.
• Step 2: Subtract the value of this angle from 360° to get the value of the corresponding reflex angle. This gives us 360° - 110° = 250°.
• Step 3: Therefore, the reflex angle is measured as 250° as seen in the figure.

We can easily notice reflex angles all around us in real life. Here is a list of a few examples of reflex angles that we come across in our day-to-day lives.

• Clock: If we observe the hands of a clock at 7 o'clock, one side of the clock forms an obtuse angle. This is the side that falls on the side of the numbers 7, 8, 9, 10, 11, 12 marked in the clock. Now, the other side which has the numbers 1, 2, 3, 4, 5, 6, forms the reflex angle.
• Pizza: In a circular pizza, if we cut a small slice and remove it, then the remaining part of the pizza forms a reflex angle.

Related Articles

Check out these interesting articles to know more about reflex angles.

• Lines and Angles - Basic Terms
• 180 Degree Angle
• Reference Angle

What is a Reflex Angle in Geometry?

An angle whose measure is greater than 180° but less than 360° is termed as a reflex angle. It is the angle that lies on the opposite side of any given acute, obtuse, and right angle. A reflex angle and its corresponding angle together form a complete angle of 360°.

What are the Examples of Reflex Angle?

All the angles that are more than 180° and less than 360° are called reflex angles. For example, 182°, 210°, 310°, and so on are reflex angles. Note that 180º and 360º are not reflex angles as they are straight angles and complete angles respectively.

What is the Difference Between an Obtuse Angle and a Reflex angle?

An obtuse angle is an angle that is more than 90° but less than 180°. A reflex angle is an angle that is more than 180° and less than 360°. So, a reflex angle is larger in size than an obtuse angle.

Is 180 Degrees a Reflex Angle?

No, 180 degrees is not a reflex angle. It is a straight angle. When the arms of an angle lie in the opposite direction, they form a straight angle of 180°. These arms make a straight line through the vertex. It is one-half of the whole turn of a circle and is called a straight angle because it looks like a straight line.

What is the Measure of Reflex Angle?

A reflex angle is more than 180° and less than 360°. In other words, a reflex angle lies between 180° and 360°.

How to Draw a Reflex Angle?

In order to draw a reflex angle, we can use the following steps. For example, let us draw a reflex angle of 240°.

• Step 1: Subtract the given reflex angle from 360°. In this case, it gives us 360° - 240° = 120°.
• Step 2: Draw and mark this angle using the protractor. Here, we need to draw an angle of 120° in the usual way.
• Step 3: After marking this angle, the angle that we get on the outside is the required angle of 240°. This is because 240° + 120° = 360° which makes a complete angle.

Can a Triangle have a Reflex Angle?

No, a triangle cannot have a reflex angle. Since the interior angles of a triangle sum up to 180°, and we know that a reflex angle measures more than 180° and less than 360°. Therefore, it is not possible for one of its angles to be a reflex angle.

Can a Quadrilateral have a Reflex Angle?

Yes, a concave quadrilateral can have one of its angles as a reflex angle. However, a convex quadrilateral cannot have a reflex angle, that is, all its interior angles are less than 180°.

How to Find a Reflex Angle?

The value of a reflex angle can be easily found if the other side of the reflex angle is known. For example, if we need to find the reflex angle of 130°, we just need to subtract it from 360°. This gives us 360° - 130° = 230°. Therefore, the reflex angle of 130° is 230° because they form a complete angle together, that is, they sum up to 360°.

What does a Reflex Angle Look Like?

A reflex angle looks like an angle greater than a semicircle. In a 2D shape, the vertex with a reflex angle points inwards. Such shapes are known as concave figures.