# Angles

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Subject classification: this is a mathematics resource. |

An angle can be defined as two rays sharing a common vertex.

## Measurement of angles

[edit | edit source]An angle is measured by considering the ratio of an arc to the radius of the arc. A scaling constant k is multiplied for various units.

- °

### Units of measurement

[edit | edit source]There are various units of measurement for measuring angles, however the most commonly used are degrees or radians.

- Degrees - It is denoted by a small circle as a superscript (°). One full rotation is considered equal to 360 degrees. Degree is subdivided into minutes and seconds as:-

1° = 60

^{'}(60 arcminutes) = 3600^{"}(3600 arcseconds)

- Radians - This is a number and is dimensionless. A full circle is equal to (pronounced two pi) radians. This in conjunction with the formula for arc length defines the historically famous irrational number (pronounced
*pi*) as,

There are six types of angles: Acute, Obtuse, Straight, Right, Reflex and Complete.

- An Acute angle is less than 90° and more than 0°
- An Obtuse angle is more than 90° and less than 180°
- A Straight angle is 180°.
- A Right angle is 90°.
- A Reflex angle is more than 180°.
- A Complete angle is 360°.

Apart from those six types of angles, we have two types of relative angles namely complementary angles and supplementary angles.

- Complementary angles are the pair of angles whose sum is equal to a right angle.
- Supplementary angles are the pair of angles whose sum is equal to a straight angle.