Definition:Angle/Directed versus Undirected

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The most basic definition of angle is an undirected angle on the interval $\left[{0^\circ \,.\,.\, 180^\circ}\right]$ or $\left[{0 \,.\,.\, \pi}\right]$.

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 $\left[{0^\circ \,.\,.\, 360^\circ}\right]$ or $\left[{0 \,.\,.\, 2 \pi}\right]$.
$(2): \quad$ 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.