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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°, π 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 19th century. Ultimately, the answer was proven to be positive: in other spaces (geometries) 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.
==Cases==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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