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.n 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.