# Types of Angles: Angle Types Based on Magnitude and Angle Types Based on Rotation (For CBSE, ICSE, IAS, NET, NRA 2022)

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There are various types of angles in geometry. Angles form the core of the geometry in mathematics. They are the fundamentals that eventually lead to the formation of the more complex geometrical figures and shapes. Let us discuss different types of angle.

When two rays combine with a common end point, where the angle is formed. The angle has two components one is βsideβ and other is βvertexβ . The side can be categorized into terminal sides and initial sides (or vertical sides) as shown in the image below.

Representation of an Angle

These two rays can combine in multiple fashions to form the different types of angles in mathematics. Let us begin by studying these different types of angles in geometry.

The parts of an angle are:

• Vertex β Point where the arms meet
• Arms β Two straight line segments from a vertex
• Angle β If a ray is rotated about its end-point, the measure of its rotation is called angle between its initial and final position

## Types of Angles

Angles can be classified into two main types:

• Based on Magnitude
• Based on Rotation

## Angle Types Based on Magnitude

In maths, there are mainly 5 types of angles based on their direction. These 5 angle types are the most common ones used in geometry. These are:

• Acute Angles
• Obtuse Angles
• Right Angles
• Straight Angles
• Reflex Angles

Angle Types Based on Magnitude

The images above illustrate certain types of angles.

### Acute Angle

An acute angle lies between 0 degrees and 90 degrees or in other words, an acute angle is one that is less than 90 degrees. The figure above illustrates an acute angle.

### Obtuse Angle

An obtuse angle is the opposite of an acute angle. It is the angle which lies between 90 degrees and 180 degrees or in other words, an obtuse angle is greater than 90 degrees and less than 180 degrees. The figure above illustrates an obtuse angle.

### Right Angle

A right angle is always equal to 90 degrees. Any angle less than 90 degrees is an acute angle whereas any angle greater than 90 degrees is an obtuse angle. The figure above illustrates a right angle or a 90-degree angle.

### Straight Angle

A straight angle is 180 degrees when measured. The figure above illustrates a straight angle or a 180-degree angle. You can see that it is just a straight line because the angle between its arms is 180 degrees.

### Reflex Angle

Since this measurement is less than 90 degrees, the arms form an acute angle. It is called a reflex angle.

Any angle that has a measure which is greater than 180 degrees but less than 360 degrees (which coincides with 0 degrees) , is a reflex angle.

## Angle Types Based on Rotation

Based on the direction of measurement or the direction of rotation, angles can be of two types:

• Positive Angles
• Negative Angles

### Positive Angles

Positive angles are those angles which are measured in a counterclockwise direction from the base. In most cases, positive angles are used to represent angles in geometry. From the origin, if an angle is drawn in the plane, it forms a positive angle.

### Negative Angles

Negative angles are those angles which are measured in a clockwise direction from the base. From the origin, if an angle is drawn towards the plane, it forms a negative angle.

## Complementary and Supplementary Angles

Apart from the aforementioned types, there are two more angle types which are complementary angles and supplementary angles. If the sum of two angles is equal to , then they are supplementary angles and if the sum is equal to , then they are called complementary angles.

Example: 1 Find the value of x, y and z

Solution:

Angle y and angle of measure are supplementary. Hence,

Solve for y

Angle x and angle of measure are supplementary. Hence,

Solve for x

The sum of angles of the triangle is equal to .

Substitute x and y by their values found above.

Solve for z.

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