Math Doubts

Zero angle

Definition

An angle that denotes null is called zero angle.

What is Zero angle?

In some cases, the angle between sides of an object or objects is null. So, a geometric concept is required to express that angle and it was introduced as zero angle in geometry. It can also be called as null angle.

There are two notable factors to understand this concept.

  1. The surface of earth is a base to everything.
  2. Every language (except very few) is written from left to right.

The concept of zero angle can be described now by considering the above two natural factors.

zero angle

The surface of earth on which we walk daily is horizontal. So, a horizontal line can be considered as a line of indicating zero angle but it should start from left and should continue its journey towards right.

Case study

The above explanation helps you to have basic knowledge on zero angle and let’s learn its concept further from a graphical example as follows.

zero angle between sides

Consider a point on the plane and denote it by a letter $\small O$. A line is started from that point. It passed through a point $\small P$ and the ray $\small \overrightarrow{OP}$ is formed geometrically. Similarly, another line is started from point $\small O$. It passed through a point $\small Q$ and the ray $\small \overrightarrow{OQ}$ is formed geometrically.

Now, let’s analyze this geometric figure to know about zero angle clearly.

The rays $\small \overrightarrow{OP}$ and $\small \overrightarrow{OQ}$ both are not parallel to the surface of earth. So, the rays $\small \overrightarrow{OP}$ and $\small \overrightarrow{OQ}$ are not representing zero angle. The rays $\small \overrightarrow{OP}$ and $\small \overrightarrow{OQ}$ have a vertex $\small O$. Therefore, an angle should be formed between them at their meeting point $\small O$ and the angle is written as $\small \angle POQ$ or $\small \angle QOP$ or $\small \angle O$.

zero angle between arms

However, the rays $\small \overrightarrow{OP}$ and $\small \overrightarrow{OQ}$ both are in same direction and have a meeting point. So, the angle between the rays $\small \overrightarrow{OP}$ and $\small \overrightarrow{OQ}$ is null, which means the angle between them is zero angle.

$\,\,\,\therefore\,\,\,\,\,\,$ $\small \angle POQ$ $\,=\,$ $\small \angle QOP$ $\,=\,$ $\small \angle O$ $\,=\,$ $0$

Notation

There are three methods to express zero angle in mathematics.

Sexagesimal system

The zero angle is written as $0^\circ$ mathematically and it is read as zero degrees.

Circular system

The zero angle is written as $0^r$ mathematically. It is simply written as $0$ in mathematics and it is read as zero radians.

Centesimal system

The zero angle is written as $0^g$ mathematically and it is read as zero gradians.