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Angles are one of the basic blocks of geometrical shapes. Reflex angle is one such type of angle which is very common in academic disciplines and real-life examples. It is an angle that lies between obtuse angles and a full rotation, i.e., a complete angle of 360 degrees. In this article, we will study some of the fascinating properties of this special angle and understand its various aspects using a diagram.

## Reflex Angle

A Reflex angle is an angle whose values lie between 180 and 360 degrees. In other words, the value of this special angle is always less than 360 degrees and always more than 180 degrees. The value of this angle always remains between a straight angle (180 degrees) and a complete angle (360 degrees). It is one of the six types of angles found in the geometrical world. The other five angles are acute angle, right angle, obtuse angle, straight angle, and complete angle. Let us understand this special angle in more detail through its definition and a diagram.

## Reflex Angle Definition

Mathematically, any angle whose value is more than 180 degrees and less than 360 degrees is a reflex angle. Simply put, the values of this angle always oscillate between 180 degrees and 360 degrees, i.e., the value of this angle always be more than an obtuse angle and always be less than a complete angle. The sum of the this angle and its corresponding angle on the other side always forms a complete angle (360 degrees).

## Reflex Angle Diagram

The shape of this particular angle can be easily understood by its diagram. The diagrammatic view of this angle will help you understand this angle more clearly. The below figure shows the diagram of this angle whose value will be between 180 degrees and 360 degrees.

## Reflex Angle Degree

For an angle to be qualified as a reflex, it must be more than 180° and less than 360°. Let X be an angle of reflex type, then X should satisfy the following condition

180°>X<360°

## Reflex Angle Formula

As we know that the value of the this angle and its corresponding angle on the other side is always 360°, hence, using this concept, we can easily find out the value of this angle. Let us comprehend this concept with an example.

Let there be an angle whose value be a.

The corresponding angle on the other side will be of reflex type

So using the above concept we can say,

reflex angle = 360° – a

It is interesting to note that this angle can be represented as a sum of straight angle (180°) and three basic angles, i.e., acute angle, right angle, and obtuse angles.

Y = Straight angle (180°) + X

where, Y = an angle that is reflex in nature

where, X can be an acute, right, or obtuse angle

## Reflex Angle Examples

As we know the value of this special angle is always greater than 180 degrees and smaller than 360 degrees. So some of its examples are 181°, 256°, 240°, 227°, 307°, 338°, 197°, 356°, 278°, etc.

## Reflex Angle Real-Life Examples

Due to its ubiquitous nature, many examples of this angle can be found in the real world. Some of these examples are listed hereunder:

- The angle between the hour hand and minute hand at 8 O’clock when measured in clockwise direction.
- The spokes that connect the wheel’s center to its passenger cabins form this angle with the horizontal as it turns.
- The angle formed by pizza slices after the removal of one slice.
- The angle created by the steering wheel and the center position can be this special angle when a car makes a quick turn.

## Reflex Angle Triangle

It is not possible to construct a triangle with a reflex angle. It is due to the fact that the sum of all the angles of triangle is exactly 180°, while the measure of this angle alone is more than 180°. So it is not possible to create such a triangle in any possible known way. But it may be noted that the exterior angles of a triangle are always reflex in nature.

## Reflex Angle Properties

Like any other geometrical entity, this special angle too have some unique features that help it to stand apart from the crowd. Using these properties of this angle, you will easily be able to solve many intricate problems related to this angle. Some of its crucial properties are given below.

- The value of this angle is always more than 180 degrees and less than 360 degrees
- This angle lies between obtuse angle and complete angle
- The exterior angle portion (remaining after extracting the interior angles) of a triangle are always reflex in nature
- It is not possible to construct a triangle having any angle of reflex type
- It can be represented as a sum of straight angle and any of the angles from acute, right, and obtuse angle
- It always occur in pairs with its corresponding angle which can be an acute, right, or an obtuse angle

## Reflex Angle Solved Examples

Some of the solved examples related to this topic is given below. By practicing these solved questions, students will have a better grasp on this topic.

**Example 1: What will be the value of the angle formed by the hands of a clock at 7 PM when measured in clockwise direction?**

Solution: As we know at 7 PM, the hour hands point to 7 and the minute hand points to 12

So the number between digits present between them in clockwise direction = 7

One digit traversal corresponds to 30°.

So the angle formed = 30 x 7

Hence, the angle formed will be 210°

**Example 2: What will be the reflex angle of 150°?**

Solution: As we know that reflex angle + other angle = 360°

Let the unknown value be X

So, X = 360° – 150°

X = 210°

**Example 3: In a triangle XYZ, the value of angle X is 50° and the value of angle Y is 60°. What will be the value of the outside angle at Z.**

Solution: As we know that, the sum of three sides of a triangle equals 180°.

Hence, X + Y + Z = 180°

50° + 60° + Z = 180°

110° + Z = 180°

Z = 180° – 110°

Z = 70°

As the outside angle will be reflex in nature, so using its formula we get

outside angle at Z= 360° – interior angle at Z

outside angle = 360° – 70°

outside angle = 290°