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- Internal_and_external_angle abstract "In geometry, an interior angle (or internal angle) is an angle formed by two sides of a polygon that share an endpoint. For a simple, convex or concave of the polygon, this angle will be an angle on the inner side of the polygon. A polygon has exactly one internal angle per vertex.If every internal angle of a simple, closed 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, closed 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, closed polygon is 180(n-2)° where n is the number of sides. The formula can by proved using mathematical induction and starting with a triangle for which the angle sum is 180°, and then adding a vertex and two sides, etc. The sum of the external angles of any simple closed (convex or concave) polygon is 360°.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 = 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 wikiPageRevisionID "589932584".
- Internal_and_external_angle hasPhotoCollection Internal_and_external_angle.
- 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 comment "In geometry, an interior angle (or internal angle) is an angle formed by two sides of a polygon that share an endpoint. For a simple, convex or concave of the polygon, this angle will be an angle on the inner side of the polygon.".
- Internal_and_external_angle label "Angle externe".
- Internal_and_external_angle label "Innenwinkel".
- Internal_and_external_angle label "Internal and external angle".
- Internal_and_external_angle label "Kąt wewnętrzny".
- Internal_and_external_angle label "Ángulo interior".
- Internal_and_external_angle label "Ângulo interno".
- Internal_and_external_angle label "زاوية داخلية".
- 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 Angle_externe.
- 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 Q1156900.
- Internal_and_external_angle sameAs Q1156900.
- Internal_and_external_angle wasDerivedFrom Internal_and_external_angle?oldid=589932584.
- Internal_and_external_angle depiction ExternalAngles.svg.
- Internal_and_external_angle isPrimaryTopicOf Internal_and_external_angle.
