Math Doubts

Formation of an Angle by the Rotation

The amount of rotation for a ray to reach its final position from its initial position is called an angle.


angle formation by rotation

A ray can be rotated in either clockwise or anticlockwise direction with a fixed endpoint. It reaches new position due to the rotation. Thus, an angle is made by a ray, once it reaches the final position from its initial position.

It is a fundamental theory to explain the formation of an angle geometrically by the rotation and it helps you to understand how an angle is formed by rotating a ray.


Let a ray is started horizontally from a point $\small R$ and it passes through a point $\small S$. Thus, a ray $\small \overrightarrow{RS}$ is formed geometrically.

formation of angle by rotation

Now, rotate the ray in either clockwise or anticlockwise direction to reach its final position. The position of the point $\small R$ is not changed but the point of the point $\small S$ is changed to point $\small T$ in the plane. Thus, the ray $\small \overrightarrow{RS}$ becomes the ray $\small \overrightarrow{RT}$.

Initially, the ray $\small \overrightarrow{RS}$ is in horizontal position and it is rotated to reach its final position $\small \overrightarrow{RT}$. Thus, an angle is made by its rotation and the angle is written as $\small \angle TRS$ or $\small \angle SRT$ in mathematics.

Math Doubts

A best free mathematics education website that helps students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved