# Zero Angle

## Definition

An angle of $0^°$ is called zero angle.

Straight lines form zero angle in geometric system and the zero angle is usually represented by $0^°$ in mathematics.

### Cases

There are two possible cases of forming zero angle geometrically.

01

### Zero angle of a Line

A straight line can form a zero angle and it is determined by considering universally acceptable two factors.

###### Parallelism

The surface of earth is base to everything. So, it is considered as reference line of zero angle. In other words, a line has $50 \%$ chance if it is parallel to surface of the earth.

###### Direction

Almost all languages are written from left to right. So, if the direction of any line is from left to right, it is has another $50 \%$ chance to become zero angle.

For example, $\overrightarrow{OP}$ is a ray.

1. It started travelling from $O$ and continued travelling from left to right through point $P$.
2. It is parallel to the surface of the earth.

Therefore, the angle made by the ray $\overrightarrow{OP}$ is an example to zero angle. Left point is assumed as starting point of both straight line and line segment.

02

#### Zero angle between Two Lines

Two straight lines can form zero angle but it is not the case of angle made by the line but it is case of angle between them. In other words, angle made by the each line with horizontal line is not considered but considers angle made by one line with another line and vice-versa.

$\overrightarrow{AB}$ and $\overrightarrow{AC}$ are two rays but each line makes an angle of $25^\circ$ with surface of the earth. The angle made by either $\overrightarrow{AB}$ or $\overrightarrow{AC}$ is not considered but measures angle of $\overrightarrow{AB}$ by considering $\overrightarrow{AC}$ as baseline to measure the angle and vice versa.

In this case, the rays $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are parallel each other, have a common vertex and in same direction. Therefore, the angle between them is zero degrees.

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