Editing Polygon (section)

===Angles===
Any polygon has as many corners as it has sides. Each corner has several angles. The two most important ones are:
* '''[[Interior angle]]''' – The sum of the interior angles of a simple ''n''-gon is {{nowrap|(''n'' − 2) × [[Pi|π]]}} [[radian]]s or {{nowrap|(''n'' − 2) × 180}} [[degree (angle)|degrees]]. This is because any simple ''n''-gon ( having ''n'' sides ) can be considered to be made up of {{nowrap|(''n'' − 2)}} triangles, each of which has an angle sum of π radians or 180 degrees. The measure of any interior angle of a convex regular ''n''-gon is <math>\left(1-\tfrac{2}{n}\right)\pi</math> radians or <math>180-\tfrac{360}{n}</math> degrees. The interior angles of regular [[star polygon]]s were first studied by Poinsot, in the same paper in which he describes the four [[Kepler–Poinsot polyhedron|regular star polyhedra]]: for a regular <math>\tfrac{p}{q}</math>-gon (a ''p''-gon with central density ''q''), each interior angle is <math>\tfrac{\pi(p-2q)}{p}</math> radians or <math>\tfrac{180(p-2q)}{p}</math> degrees.<ref>{{cite book |last=Kappraff |first=Jay |title=Beyond measure: a guided tour through nature, myth, and number |publisher=World Scientific |year=2002 |page=258 |isbn= 978-981-02-4702-7 |url=https://books.google.com/books?id=vAfBrK678_kC&q=star+polygon&pg=PA256}}</ref>
* '''[[Exterior angle]]''' – The exterior angle is the [[supplementary angle]] to the interior angle. Tracing around a convex ''n''-gon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the polygon makes one full [[Turn (geometry)|turn]], so the sum of the exterior angles must be 360°. This argument can be generalized to concave simple polygons, if external angles that turn in the opposite direction are subtracted from the total turned. Tracing around an ''n''-gon in general, the sum of the exterior angles (the total amount one rotates at the vertices) can be any integer multiple ''d'' of 360°, e.g. 720° for a [[pentagram]] and 0° for an angular "eight" or [[antiparallelogram]], where ''d'' is the [[Density (polytope)#Polygons|density]] or [[turning number]] of the polygon.