Angle – Definition, Facts, Types, Properties, Examples | How to Draw and Measure an Angle?

The measurement between the two lines is called an “Angle”. It is formed in between the common point of two rays. Also, the rays are known as the arms of the angle. The symbol used to represent an angle is ‘∠’. The angle is measured in degrees such as 30°, 45°, 60°, 90°, 180°. Also, another way to represent an angle in radians. It is called pi (π). Read on the article to know the definition of angle, types of angles, properties, parts of an angle, how to measure angle along with few examples.

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What is Angle in Maths?

A Figure formed by two rays or lines sharing a common endpoint is known as Angle. The common end where two rays meet is called a node or vertex. It is denoted using the symbol ∠. Some greek letters like θ, α, β, etc are also used to represent an angle.


Properties of Angles

Check out the important properties of angles given below. Make a note of these angles for further preferences.

  • The sum of all the angles on one side of a straight line is equal to 180 degrees,
  • Also, the sum of all the angles around the point is equal to 360 degrees.

Parts of Angles

An angle consists of different parts such as vertex, arms, Initial Side, and Terminal Side. They are given below

Parts of an angle

Vertex: The endpoints of an angle are called vertex. It is the endpoint where two rays meet.
Arms: The sides of an angle are known as arms of the angles. An angle has two sides.
Initial Side: The Initial Side is also called a Reference line. While taking measurements, all the measurements are taken using this reference line.
Terminal Side: Terminal Side is the side where the angle measurement is done.

Angle Measurement

Angle measurement is done using three units of angle measurements. They are explained below

Degree of an Angle

The degree of an Angle is represented as ‘°’. The angle is considered as 1° if the rotation is from the initial point to the terminal side is equal to 1/360 of the full rotation. Also, the degree is divided into minutes and seconds.
1°= 60′ = 3600”

Degree of an angle

Radian of an Angle

Radian of an Angle is nothing but the SI unit of angle. All the derivatives and integrals can be calculated in radians and denoted by ‘rad’. When you consider a full complete circle, then there will be 2π radians available.
360 = 2π
1 radian = 180°/π

Radian of an angle

Gradian of an Angle

Gradian of an Angle is known as gon or a grade. The angle is equal to 1 gradian when the rotation starts from the initial point to the terminal side is 1/400 of the full rotation.

How to Label the Angles?

Two different ways are available to label the angles. They are

1. By giving a name to the angle using small letters.
2. Also, by using the three letters on the shapes. The middle letter represents the vertex of an angle. Example ∠ABC = 60°.

How to Measure an Angle?

The Angle Measurement is calculated using a tool called protractor. It consists of two sets of numbers that appear in two opposite directions. One set goes from 0 to 180 degrees and the other set is from 180 to 0 degrees.

Types of Angles

There are different types of angles available depends on based on their measure of the angle. They are

1. Acute angle
2. Right angle
3. Obtuse angle
4. Straight angle
5. Reflex angle
6. Full Rotation

1. Acute angle

An angle that measures between 0° to 90° is called an Acute angle. From the picture below, the angle formed by the intersection of AB and BR at B forms an angle ABC which measures 35°. Thus, ABC is called an acute angle.

Acute Angle

2. Right Angle

The Right Angle is an angle that measures exactly 90°. At a right angle, the two lines are perpendicular to each other. In the figure below, line AB intersects line BC at B and forms an angle ABC which measures 90°.

right angle

3. Obtuse Angle

The Obtuse Angle is an angle that measures greater than 90°. An Obtuse Angle lies between 90° and 180°.
Obtuse Angle Measure = (180 – acute angle measure)
In the figure below, line AB intersects line BC at B and forms an angle ABC which measures 140°. Thus, ABC is called an obtuse angle.

Obtuse Angle

4. Straight Angle

A straight angle is an angle that measures 180° is called a straight angle. It looks like a straight line.

Straight Angle

5. Reflex Angle

The Reflex Angle lies between greater than 180° and less than 360°. Also, the reflex angle is completely complementary to the acute angle on the other side of the line.
A Measure of Acute Angle = 360° – a Measure of Reflex Angle

Reflex Angle

6. Full Rotation

The Full rotation of angle that is equal to 360 degrees is called Full Rotation.

Different Types of an Angles

Check out the below table to know all the angles and their description in a single place.

Type of angles Description
Acute Angle < 90°
Right Angle = 90°
Obtuse Angle > 90°
Straight Angle =180°
Reflex Angle >180°
Full rotation/complete angle =360°

Interior and Exterior Angles

In a polygon, we can see both interior and exterior angles. Interior angles are that lie inside the polygon in a closed shape with angles and sides. Also, the exterior angles are present on the outside of the shape. The exterior angles are present between the sidelines and extended from adjacent sides.

Interior and Exterior Angles

Complementary & Supplementary Angles

If you get 90° by adding two angles, then those two angles are called Complementary angles. The Complementary angles must not present adjacent to each other.

From the given figure, a and b the angels are present adjacent to each other and the addition will be up to 90°. Therefore, they are known as complementary angles. Also, if you consider c and d, the angles are not adjacent to each other, but they also add up to 90° and they are also known as complementary angles.

When two angles add up to form a 180° then they are known as supplementary angles.

Read More: Complementary and Supplementary Angles

Positive & Negative Angles

A positive Angle is an angle measured in an Anti-Clockwise direction. Negative Angle is an angle measured in Clockwise direction is Negative Angle.

Positive & Negative Angles

Frequently Asked Questions on Angles

1. What is an angle?

An angle is formed by joining two rays at the joint at a single point. The two rays to form an angle are known as arms or sides of the angle and the common point is the vertex of an angle.

2. What are the main six types of angles?

The main types of angles are
(i) Acute angle
(ii) Right angle
(iii) Obtuse angle
(iv) Straight angle
(v) Reflex angle
(vi) Full rotation

3. What is a zero angle?

The Zero angle is an angle that measures zero degrees.

4. How angles are measured?

The angles are measured using a tool named a protractor.

5. What are the properties of angles?

The properties of angles are
(i) The sum of all the angles around a point always measures 360 degrees.
(ii) Also, the sum of all the angles on one side of a straight line always measures 180 degrees.

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