Definition:Conjugate Angles

Definition
The conjugate of an angle $\theta$ is the angle $\phi$ such that $\theta + \phi = 2 \pi$.

That is, it is the angle that makes the given angle equal to a full angle.

The angle $2 \pi - \theta$ is also known as the explement or explementary angle of (or for, or to) $\theta$.

Note
Obviously, this is defined in terms of radians. The equivalent statement in terms of degrees would replace every $2 \pi$ with $360^\circ$.