# Angle Measurement: What is Angle? Positive and Negative Angles: Measurement of Angle (For CBSE, ICSE, IAS, NET, NRA 2022)

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# Title: Angle Measurement

- The concepts of equality, sums, and differences of angles are important and used throughout geometry, but the subject of trigonometry is based on the
*measurement*of angles. - A ray is named after the endpoint and another point on the ray e. g.

## What is Angle?

- The angle that is formed between two rays with the same endpoint is measured in degrees.
- That point is called the vertex.

It is written as ∡ CAB

## Positive and Negative Angles

- An angle formed by a rotating ray is said to be positive or negative depending on whether its moves anticlockwise or clockwise direction respectively.
- Positive angle: if the direction of rotation is anticlockwise
- Negative angle: if the direction of rotation is clockwise

## Measurement of Angle

- A complete revolution, i.e.. when the initial and terminal sides are in the same position after rotating clockwise or anticlockwise, is divided into 360 units called
*degrees*. - Therefore, if the rotation from the initial side to the terminal side is of a revolution, then the angle is said to have a measure of one degree.
- It is denoted as

## Examples

## Degree Measurement

- This is also called an English system.
- Radian measure is slightly more complex than the degree measure. Imagine a circle with a radius of 1 unit.
- After that imagine an arc of the circle having a length of 1 unit.
- Angle subtended by this arc at the center of the circle has a measure of 1 radian.