# Definition:Conjugate Angles

## Definition

The conjugate of an angle $\theta$ is the angle $\phi$ such that:

$\theta + \phi = 2 \pi$

where $\theta$ and $\pi$ are expressed in radians.

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

Equivalently, the conjugate of an angle $\theta$ is the angle $\phi$ such that:

$\theta + \phi = 360 \degrees$

where $\theta$ and $\pi$ are expressed in degrees.

Thus, conjugate angles are two angles whose measures add up to the measure of $4$ right angles.

That is, their measurements add up to $360$ degrees or $2 \pi$ radians.

## Also known as

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

## Also see

• Results about conjugate angles can be found here.