Representation of an angle

Definition

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

Introduction

Geometrically, an angle is formed between its sides when two straight lines meet at a point and we have learned how to denote it graphically but it becomes tough to express an angle graphically every time.

So, a notation is essential for us to represent an angle easily in mathematics and it is called the representation of an angle. Now, let’s learn the mathematical notation of an angle.

Example

Let’s denote the meeting point of the two lines by $O$, assume that one ray is passed through a point $P$ and the second ray is passed through a point $Q$.

The symbol $\angle$ is used to represent an angle in mathematics. Now, the graphical representation of an angle is appearing with three points.

There are two different ways to express an angle in mathematics and let’s learn both methods to know the mathematical notation of an angle.

Three Point form

The angle can be expressed mathematically in the form of three points. However, it is possible to represent an angle in three points in two ways.

In clockwise direction, the first point is $P$, the second point is $O$ and third point is $Q$. So, the angle should be expressed in three points, whereas we should follow same order while writing an angle.

Therefore, the $angle \, POQ$ is written as $\angle POQ$ in mathematics.

In anticlockwise direction, the first point is $Q$, the second point is $O$ and third point is $P$. So, the angle should also be expressed in three points and we should follow same order while expressing an angle.

Therefore, the $angle \, QOP$ is written as $\angle QOP$ in mathematics.

Remember that you can consider any one of them while representing an angle in three points form. Therefore, the angle can be written in three points form as $\angle POQ$ or $\angle QOP$.

Single Point form

An angle is formed at a meeting point of two straight lines. So, an angle can be simply represented in the form of the vertex of an angle.

In this example, the vertex of angle is $O$. So, the angle is read as $angle \, O$ simply and it can be written as $\angle O$ in mathematics.

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