\begin{definition}[Definition:Angle/Directed versus Undirected]
The most basic definition of angle is an undirected angle on the interval $\closedint {0 \degrees} {180 \degrees}$ or $\closedint 0 \pi$.
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:
:$(1): \quad$ Undirected angles on the interval $\closedint {0 \degrees} {360 \degrees}$ or $\closedint 0 {2 \pi}$.
:$(2): \quad$ Directed angles, with the positive direction being anticlockwise 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 $720 \degrees$ degree spin in skateboarding, skiing, etc.
Category:Definitions/Angles
\end{definition}