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.

\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 $2\pi$ (pronounced two pi) radians. This in conjunction with the formula for arc length defines the historically famous irrational number $\pi$ (pronounced pi) as,

$\pi=\frac{1}{2}\frac{circumference~of~a~circle}{radius~of~the~circle}$

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

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°.

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