Definition:Angle/Directed versus Undirected

Definition
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.