# Formation of an angle by Rotation

## Definition

The formation of an angle by the rotation of a line from its initial position to final position is called an angle formed by the rotation.

A straight line can make an angle geometrically when it is rotated to a particular position from its initial position. There is an angle formed between initial and final positions of the line but it is formed by the rotation. Therefore, the angle is known as an angle formed by rotation.

### Examples

The following two examples demonstrate well to understand how angles are formed geometrically by the rotation.

#### Example: 1

A ray is called as $\overrightarrow{RS}$ at its initial position and it is rotated in anticlockwise direction to reach its final position where it is called as the ray $\overrightarrow{RT}$.

An angle, denoted by $\angle SRT$ is formed when the ray reached its final position from its initial position.

The angle is actually formed by the rotation. Hence, the angle $SRT$ is known as an angle formed by the rotation.

#### Example: 2

Another ray is called as $\overrightarrow{UV}$ at its initial position and then it is rotated in clockwise direction at its final position where it is called as the ray $\overrightarrow{UW}$.

An angle, represented as $\angle VUW$ is formed geometrically when the ray $\overrightarrow{UV}$ become $\overrightarrow{UW}$ by the rotation.

The angle $VUW$ is actually formed by the rotation. Therefore, the $\angle VUW$ is called an angle formed by rotation.

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