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.

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