Sum of angles of a triangle Sum of angles of a triangle In several geometries, a triangle has three "vertices" and three "sides", where three angles of a triangle are formed at each vertex by a pair of adjacent sides. In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180 °, radians, two right angles, or a half-turn. It was unknown for a long time whether other geometries exist, where this sum is different. The influence of this problem on mathematics was particularly strong during the 19th century. Ultimately, the
Angles at the centre of the Angle homeland in the northeastern portion of the modern German "Bundesland" of Schleswig-Holstein, on the Jutland Peninsula. There, a small peninsular area is still called Anglia today and is formed as a triangle drawn roughly from modern Flensburg on the Flensburger Fjord to the City of Schleswig and then to Maasholm, on the Schlei inlet. Attribution: Angles The Angles () were one of the main Germanic peoples who settled in Great Britain in the post-Roman period. They founded several of the kingdoms of Anglo-Saxon England, and their name is the root of the name England.