**Angle Meaning**

The amount of rotation about the point of intersection of two planes (or lines) which is required to bring one in correspondence with the other is called an **Angle**. There are many different types of angles which we will study in this article.

### Angle Definition

In the angle ∠ABC(Like given above), it is generally represented by Greek letters such as θ, α, β etc.

It can also be represented by three letters of the shape that define the angle, with the middle letter being where the angle actually is (i.e.its vertex).

*Eg. ∠ABC, where B is the given angle.*

**Angle measurement** terms are – degree °, radians or gradians.

**Types of Angles**

- Acute Angle – 0° to 90°, both exclusive.
- Obtuse Angle – 90° to 180°, both exclusive.
- Right Angle – Exactly 90°.
- Straight Angle – Exactly 180°.
- Reflex Angle – 180° to 360°, both exclusive.
- Full Rotation – Exactly 360°

Type of angles |
Description |

Acute Angle |
An Angle less than 90° |

Obtuse Angle |
An Angle greater than 90° |

Right Angle |
An Angle equal to 90°. |

Straight Angle |
An Angle which is exactly 180°. |

Reflex Angle |
An Angle greater than 180° |

**Positive & Negative Angles**

- Positive Angle- An Angle measured in Anti-Clockwise direction is
**Positive Angle**. - Negative Angle- An angle measured in Clockwise direction is
**Negative Angle**.

**Parts of Angles**

**Vertex-**The corner points of an angle is known as Vertex. It is the point where two rays meet.**Initial Side –**It is also known as the reference line. All the measurements are done taking this line as the reference.**Terminal Side-**It is the side (or ray) up to which the angle measurement is done.

**Angle Measurement**

To measure everything in this world, we need a unit in a similar angle measurement requires three units of measurement :

### Degree of an Angle

It is represented by ° (read as a degree). It most likely comes from Babylonians, who used a base 60 (Sexagesimal) number system. In their calendar, there was a total of 360 days. Hence, they adopted a full angle to be 360°. First, they tried to divide a full angle into angles using the angle of an equilateral triangle. Later, following their number system (base 60), they divided 60° by 60 and defined that as 1°. Sometimes, it is also referred to as arc degree or arc-degree which means the degree of an arc.

An angle is said to be equal to 1° if the rotation from the initial to the terminal side is equal to 1/360 of the full rotation.

A degree is further divided into minutes and seconds. 1′ (1 minute) is defined as one-sixtieth of a degree and 1” (1 second) is defined as one-sixtieth of a minute. Thus,

1°= 60′ = 3600”

Angle Measurement in Degrees

**Radian of an Angle**

This is the SI unit of angle. Radian is mostly used in Calculus. All the formula for derivatives and integrals hold true only when angles are measured in terms of a radian. It is denoted by ‘rad’.

The length of the arc of a unit circle is numerically equal to the measurement in radian of the angle that it subtends.

In a complete circle, there are 2π radians.

360 = 2π; radian

Therefore, 1 radian = 180°/π

**Gradian of an Angle**

This unit is least used in Maths. It is also called a gon or a grade.

An angle is equal to 1 gradian if the rotation from the initial to terminal side is 1/400 of the full rotation. Hence, the full angle is equal to 400 gradians.

It is denoted by ‘grad’.

Figure 3 shows the example of angles in gradian.

Figure 3: Angle Measurement in Gradian

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