Definition:Angle

Definition
Given two intersecting lines or line segments, the amount of rotation about the intersection required to bring one into correspondence with the other is called the angle between them.



Types of Angle
Angles can be divided into categories:
 * Zero angle
 * Acute angles
 * Right angles
 * Obtuse angles
 * Straight angles
 * Reflex angles
 * Full angles

It is possible to have angles outside the $[0^\circ. . 360^\circ ]$ or $[0. . 2 \pi ]$ range, but in geometric contexts it is usually preferable to convert these to angles inside this range by adding or subtracting multiples of $360^\circ$ or $2\pi$.

Directed versus Undirected Angles
The most basic definition of angle is an undirected angle on the interval $[0^\circ. . 180^\circ]$ or $[0. . \pi]$. This definition is often insufficient, in cases such as the external angles of a polygon. Therefore, angles are most commonly defined in one of two ways:
 * Undirected angles on the interval $[0^\circ . . 360^\circ ]$ or $[0 . . 2\pi ]$.
 * Directed angles, with the positive direction being counterclockwise from a given line (or, if no line is specified, from the x-axis). This definition is more commonly found in applied mathematics, such as in surveying, navigation, or, more colloquially, in a $720^\circ$ degree spin in skateboarding, skiing, etc.

Note
It is advisable to use radians, especially in calculus, since the derivatives of trigonometric functions work out without the necessity of multiplicative constants when angles are measured in radians (such as $\dfrac{d}{dx}\sin x=\cos x$).

Also see

 * Solid Angle