# Angles

 Subject classification: this is a mathematics resource.

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

## Measurement of angles

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.

${\displaystyle \theta ={\frac {s}{r}}(k)}$°

### Units of measurement

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 ${\displaystyle 2\pi }$ (pronounced two pi) radians. This in conjunction with the formula for arc length defines the historically famous irrational number ${\displaystyle \pi }$ (pronounced pi) as,
${\displaystyle \pi ={\frac {1}{2}}{\frac {circumference~of~a~circle}{radius~of~the~circle}}}$

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

1. An Acute angle is less than 90° and more than 0°
2. An Obtuse angle is more than 90° and less than 180°
3. A Straight angle is 180°.
4. A Right angle is 90°.
5. A Reflex angle is more than 180°.
6. 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.

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