page_title: Sum of angles of a triangle
section_title: Exterior angles
hierarchical_section_title: Sum of angles of a triangle / Exterior angles
caption_attribution_description: Français&#160;: La somme des mesures des angles d'un triangle est l'angle plat. Ceci se montre facilement en traçant la parallèle à un des côté passant par le sommet opposé, et en considérant l'égalité des angles alterne-internes et des angles correspondants (c'est la preuve d'Euclide dans ses Éléments, I-32). Auteur&#160;: Christophe Dang Ngoc Chan, réalisé avec un programme de dessin vectoriel. Licence GFDL Christophe Dang Ngoc Chan
context_page_description: In a Euclidean space, the sum of angles of a triangle equals the straight angle.
  A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.
  It was unknown for a long time whether other geometries exist, for which this sum is different. The influence of this problem on mathematics was particularly strong during the 19th century. Ultimately, the answer was proven to be positive: in other spaces this sum can be greater or lesser, but it then must depend on the triangle. Its difference from 180° is a case of angular defect and serves as an important distinction for geometric systems.
context_section_description: Angles between adjacent sides of a triangle are referred to as interior angles in Euclidean and other geometries. Exterior angles can be also defined, and the Euclidean triangle postulate can be formulated as the exterior angle theorem. One can also consider the sum of all three exterior angles, that equals to 360° in the Euclidean case (as for any convex polygon), is less than 360° in the spherical case, and is greater than 360° in the hyperbolic case.
caption: The picture shows exterior angles along with interior ones, for the rightmost vertex it is shown as =/)
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