# Representation of an Angle

## Definition

A method of expressing an angle in mathematical form is called the representation of an angle.

In geometry, there is a procedure to express any angle in mathematics.

The symbol $\angle$ is used to represent an angle symbolically. Additionally, the names of three points are written one after one, after the angle symbol to express the angle in mathematical form meaningfully.

One of three points is vertex of the angle and it is written in the middle to express where the angle is actually formed. The remaining two points are any one point of the two lines.

### Example

The following two examples understand you how to denote any angle geometrically in mathematics.

#### Example: 1

At point $L$ on the plane, two rays formed an angle. $M$ is any point of one line and $N$ is any point on the second line.

The names of three points $L$, $M$ and $N$ are used to represent the angle but the name of the point $L$ is written middle to remaining two points because, the angle is formed at point $L$ and it is known as vertex of the angle.

1. This angle is called as $angle \, MLN$ and denoted as $\angle MLN$.
2. This angle is also called as $angle \, NLM$ and written as $\angle NLM$.
3. The angle is actually formed by the rays at point $L$. So, this angle is also called as $angle \, L$ and expressed as $\angle L$ in mathematics.

The representation of three methods is same and representing same angle.

Therefore, $\angle MLN = \angle NLM = \angle L$

#### Example: 2

Two rays formed an angle at point $O$. $P$ is any point of the first line and $Q$ is any point on the second line.

1. The angle is written as $\angle POQ$ and it is read as $angle \, POQ$.
2. The angle is also written as $\angle QOP$ and it is read as $angle \, QOP$.
3. The angle is also written as $\angle O$ simply and it is read as $angle \, O$.

The three methods represents the same angle in mathematical form.

Therefore, $\angle POQ = \angle QOP = \angle O$

Now, express any angle in mathematical form in any one of three methods and read it on the basis these two examples.