Editing Internal and external angles (section)

{{short description|Supplementary pair of angles at each vertex of a polygon}}
{{Redirect|Interior angle|interior angles on the same side of the transversal|Transversal line}}
{{More citations needed|date=November 2023}}
[[File:Internal and external angles.png|thumb|upright=1.25|The corresponding internal (teal) and external (magenta) angles of a polygon are supplementary (sum to a half [[Turn (angle)|turn]]). The external angles of a non-self-intersecting closed polygon always sum to a full turn.]]
{{Angles}}
[[Image:ExternalAngles.svg|thumb|upright=1.25|right|Internal and external angles]]

In [[geometry]], an [[angle]] of a [[polygon]] is formed by two adjacent [[edge (geometry)|sides]].  For a [[simple polygon]] (non-self-intersecting), regardless of whether it is [[Polygon#Convexity and non-convexity|convex or non-convex]], this angle is called an '''internal angle''' (or interior angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per [[vertex (geometry)|vertex]].

If every internal angle of a simple polygon is less than a [[straight angle]] ([[pi|{{mvar|π}}]] [[radian]]s or 180°), then the polygon is called [[convex polygon|convex]].

In contrast, an '''external angle''' (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a [[Extended side|line extended from an adjacent side]].<ref name=PL>Posamentier, Alfred S., and Lehmann, Ingmar. ''[[The Secrets of Triangles]]'', Prometheus Books, 2012.</ref>{{rp|pp. 261–264}}