An exterior angle of a polygon is an angle formed between one side of the polygon and the extension of an adjacent side. An $n\text{-}$sided polygon has $2n$ exterior angles, two at each vertex. In a convex polygon, each exterior angle lies outside the polygon and forms a linear pair with its corresponding interior angle. This means that each exterior angle is supplementary to its interior angle.

Interior Angle	Corresponding Exterior Angles	Sum of Measures
$\angle 11$	$\angle 1$ and $\angle 2$	$m\angle 1+m\angle 11=180^{\circ }$ $m\angle 2+m\angle 11=180^{\circ }$
$\angle 12$	$\angle 3$ and $\angle 4$	$m\angle 3+m\angle 12=180^{\circ }$ $m\angle 4+m\angle 12=180^{\circ }$
$\angle 13$	$\angle 5$ and $\angle 6$	$m\angle 5+m\angle 13=180^{\circ }$ $m\angle 6+m\angle 13=180^{\circ }$
$\angle 14$	$\angle 7$ and $\angle 8$	$m\angle 7+m\angle 14=180^{\circ }$ $m\angle 8+m\angle 14=180^{\circ }$
$\angle 15$	$\angle 9$ and $\angle 10$	$m\angle 9+m\angle 15=180^{\circ }$ $m\angle 10+m\angle 15=180^{\circ }$

In contrast, when polygon is concave, some exterior angles might lie inside the polygon. In this case, the measures of those angles are considered to be negative.

In any case, the Polygon Exterior Angles Theorem guarantees that the sum of the measures of the exterior angles is always equal to $360^{\circ }.$