An exterior angle β of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2π - α, where α is the corresponding internal angle between two adjacent sides. Consider the angles γ_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 γ is known as an exterior angle bisector, while a bisector of an angle β (which is simply a line oriented in the opposite direction as the interior angle bisector) is not given any special name.
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