How does the sign of an angle's measure determine its direction of rotation

Angles are conventionally measured counterclockwise from the positive x-axis. An angle with a negative sign is measured in the opposite direction (clockwise from the positive x-axis).


You need to be a little careful with navigation angles (bearings). Bearings are usually measured clockwise from North, so a negative bearing angle would be in the counterclockwise direction from North.

In mechanics problems, angles are often designated with respect to some reference line or plane and the positive direction specified (or chosen). Then an angle having a negative sign will be one that is in the direction opposite the one specified (or chosen) as positive.