Internal and external angle
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.
If every internal angle of a simple polygon is less than 180°, the polygon is called convex.
In contrast, an exterior angle (or external angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.
The sum of the internal angle and the external angle on the same vertex is 180°.
The sum of all the internal angles of a simple polygon is 180(n-2)° where n is the number of sides. The formula can be proved using mathematical induction and starting with a triangle for which the angle sum is 180°, then replacing one side with two sides connected at a vertex, and so on.
