Editing Internal and external angles (section)

==Properties==
* The sum of the internal angle and the external angle on the same vertex is {{mvar|π}} radians (180°).
* The sum of all the internal angles of a simple polygon is {{math|''π''(''n'' − 2)}} radians or {{math|180(''n'' − 2)}} degrees, where {{mvar|n}} is the number of sides. The formula can be proved by using [[mathematical induction]]: starting with a triangle, for which the angle sum is 180°, then replacing one side with two sides connected at another vertex, and so on.
* The sum of the external angles of any simple polygon, if only one of the two external angles is assumed at each vertex, is {{math|2''π''}} radians (360°).
* The measure of the exterior angle at a vertex is unaffected by which side is extended: the two exterior angles that can be formed at a vertex by extending alternately one side or the other are [[vertical angles]] and thus are equal.