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Exterior Angle


ExteriorAngles

An exterior angle beta of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2pi-alpha, where alpha is the corresponding internal angle between two adjacent sides (Zwillinger 1995, p. 270).

ExteriorAnglesDelta

Consider the angles gamma_i formed between a side of a polygon and the extension of an adjacent side. Since there are two directions in which a side can be extended, there are two such angles at each vertex. However, since corresponding angles are opposite, they are also equal.

Confusingly, a bisector of an angle gamma is known as an exterior angle bisector, while a bisector of an angle beta (which is simply a line oriented in the opposite direction as the interior angle bisector) is not given any special name.

The sum of the angles gamma_i in a convex polygon is equal to 2pi radians (360 degrees), since this corresponds to one complete rotation of the polygon.


See also

Angle, Complementary Angles, Exterior Angle Bisector, Exterior Angle Theorem, Regular Polygon, Supplementary Angles, Vertex Angle

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References

Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, 1995.

Referenced on Wolfram|Alpha

Exterior Angle

Cite this as:

Weisstein, Eric W. "Exterior Angle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ExteriorAngle.html

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