Directed Angles Instead of Casework

A directed angle is an angle with a sign depending on its direction. We usually say that an angle is positive if it reads counterclockwise and negative if it reads clockwise. For example, in the diagram shown below, the $\measuredangle ABC = 60^\circ$ since rotating $AB$ onto $BC$ creates a positive rotation (or counterclockwise rotation). $\measuredangle CBA =-60^\circ$ since rotating $CB$ onto $BA$ creates a negative rotation (or clockwise rotation)

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