# Zero angle

## Definition

An angle of zero degrees is called zero angle.

### Representation

The zero angle is usually represented in three different forms mathematically.

1. Zero degrees, written as $0^\circ$.
2. Zero radians, written as $0$.
3. Zero gradians, written as $0^g$.

It is time to study the geometrical formation of zero angle.

## Formation

There are two possible cases of forming zero angle in geometrical system.

#### Zero angle of a Line

The zero angle of a straight line is determined by considering two factors.

###### Parallelism

The surface of earth is base to everything and everyone. So, it is considered as a reference line for zero angle.

###### Direction

Almost all languages are written from left to right hand side. So, the direction of forming zero angle of a line should be same.

##### Example

$\overrightarrow{OP}$ is a ray. Actually, the starting point of this ray is at left side and also parallel to the surface of the earth. Therefore, the ray $\overrightarrow{OP}$ represents a zero angle.

#### Zero angle between Two Lines

When two lines are in same direction with a vertex, then there is no angle between them. Therefore, the angle between them is a zero angle.

##### Example

$A$ is a point in a plane. A ray is started from point $A$ and passes through the point $B$. Similarly, another ray is also started from point $A$ and it passes through the point $C$. Thus, the rays $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are formed geometrically.

In this case, the angle of each ray is $25^\circ$ with surface of the earth.

1. The two lines have common starting point.
2. The two lines are in same direction.

It represents that the two rays are parallel lines. So, there is no angle between them even through each ray makes an angle of $25$ degrees. In this case, $\overrightarrow{AB}$ is considered as a reference line to measure the angle of $\overrightarrow{AC}$ and vice-versa.

$\angle CAB = \angle BAC = 0^\circ$

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