# Definition:Conjugate Angles

Jump to navigation
Jump to search

## 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

## Sources

- 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**conjugate angles** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**conjugate angles**