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• Internal_and_external_angle abstract "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. The sum of the external angles of any simple convex or non-convex polygon is 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.The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles. In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n-2k)° where n is the number of vertices and k = 0, 1, 2, 3 ... represents the number of total revolutions of 360° one undergoes walking around the perimeter of the polygon. In other words, 360k° represents the sum of all the exterior angles. For example, for ordinary convex and concave polygons k = 1, since the exterior angle sum is 360°, and one undergoes only one full revolution walking around the perimeter.".
• Internal_and_external_angle thumbnail ExternalAngles.svg?width=300.
• Internal_and_external_angle wikiPageExternalLink star_pentagon.html.
• Internal_and_external_angle wikiPageExternalLink triangleinternalangles.html.
• Internal_and_external_angle wikiPageID "524003".
• Internal_and_external_angle wikiPageLength "3243".
• Internal_and_external_angle wikiPageOutDegree "17".
• Internal_and_external_angle wikiPageRevisionID "677818788".
• Internal_and_external_angle wikiPageWikiLink Angle.
• Internal_and_external_angle wikiPageWikiLink Category:Angle.
• Internal_and_external_angle wikiPageWikiLink Category:Elementary_geometry.
• Internal_and_external_angle wikiPageWikiLink Category:Euclidean_plane_geometry.
• Internal_and_external_angle wikiPageWikiLink Category:Polygons.
• Internal_and_external_angle wikiPageWikiLink Convex_polygon.
• Internal_and_external_angle wikiPageWikiLink Directed_angles.
• Internal_and_external_angle wikiPageWikiLink Geometry.
• Internal_and_external_angle wikiPageWikiLink Interior_(topology).
• Internal_and_external_angle wikiPageWikiLink Mathematical_induction.
• Internal_and_external_angle wikiPageWikiLink Polygon.
• Internal_and_external_angle wikiPageWikiLink Star_polygon.
• Internal_and_external_angle wikiPageWikiLink Vertex_(geometry).
• Internal_and_external_angle wikiPageWikiLink File:ExternalAngles.svg.
• Internal_and_external_angle wikiPageWikiLinkText "Internal and external angle".
• Internal_and_external_angle wikiPageWikiLinkText "exterior angle".
• Internal_and_external_angle wikiPageWikiLinkText "external angle".
• Internal_and_external_angle wikiPageWikiLinkText "external".
• Internal_and_external_angle wikiPageWikiLinkText "interior angles".
• Internal_and_external_angle wikiPageWikiLinkText "internal".
• Internal_and_external_angle wikiPageUsesTemplate Template:Redirect.
• Internal_and_external_angle wikiPageUsesTemplate Template:Reflist.
• Internal_and_external_angle wikiPageUsesTemplate Template:Rp.
• Internal_and_external_angle subject Category:Angle.
• Internal_and_external_angle subject Category:Elementary_geometry.
• Internal_and_external_angle subject Category:Euclidean_plane_geometry.
• Internal_and_external_angle subject Category:Polygons.
• Internal_and_external_angle type Polytope.
• Internal_and_external_angle comment "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.".
• Internal_and_external_angle label "Internal and external angle".
• Internal_and_external_angle sameAs Q1156900.
• Internal_and_external_angle sameAs زاوية_داخلية.
• Internal_and_external_angle sameAs Angle_interior.
• Internal_and_external_angle sameAs Innenwinkel.
• Internal_and_external_angle sameAs Ángulo_interior.
• Internal_and_external_angle sameAs Barne_angelu.
• Internal_and_external_angle sameAs Sisä-_ja_ulkokulma.
• Internal_and_external_angle sameAs זווית_חיצונית.
• Internal_and_external_angle sameAs 내각과_외각.
• Internal_and_external_angle sameAs Kąt_wewnętrzny.
• Internal_and_external_angle sameAs Ângulo_interno.
• Internal_and_external_angle sameAs m.02lcn5.
• Internal_and_external_angle sameAs Unghi_interior.
• Internal_and_external_angle sameAs มุมภายในและมุมภายนอก.
• Internal_and_external_angle sameAs Внутрішній_кут.
• Internal_and_external_angle sameAs Q1156900.
• Internal_and_external_angle sameAs 內角和外角.
• Internal_and_external_angle wasDerivedFrom Internal_and_external_angle?oldid=677818788.
• Internal_and_external_angle depiction ExternalAngles.svg.
• Internal_and_external_angle isPrimaryTopicOf Internal_and_external_angle.