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# explementary

The explementary arc of an arc $a$ of a circle is the arc forming together with $a$ the full circle.

Two angles are called explementary angles of each other, if their sum is the full angle $2\pi$, i.e. $360^{\circ}$. In the below picture, the interior angle $\alpha=60^{\circ}$ of an equilateral triangle and its explementary angle $\beta=300^{\circ}$ (which is an exterior angle of the triangle) are seen.

Defines:

explementary angle, explementary arc, full angle

Related:

ComplementaryAngles

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Definition

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## Mathematics Subject Classification

51M04*no label found*51F20

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## Comments

## Explementary angle

Just want to make sure I understand this correctly: let's say alpha is the interior angle of an equilateral triangle in normal (Euclidean) space. The explementary angle of that angle would be 300 degrees, right?

## Re: Explementary angle

Yes, the explementary angle of any 60-degree angle is 300 degrees.

## Re: Explementary angle

and since you are here, you can add "supplementary angle" definition

## Re: Explementary angle

A picture would help, imho. Preferably two unequal angles: MathNerd's equilateral triangle example would probably work nicely. Yay!