Isosceles triangle is acute, right or obtuse depends only on the angle at its apex. In Euclidean geometry, the base angles cannot be obtuse (greater than 90°) or right (equal to 90°) because their measures would sum to at least 180°, the total of all angles in any Euclidean triangle. Since a triangle is obtuse or right if and only if one of its angles is obtuse or right, respectively, an isosceles triangle is obtuse, right or acute if and only if its apex angle is respectively obtuse, right or acute. In Edwin Abbott's book "Flatland", this classification of shapes was used
Sum of angles of a triangle to zero. For a spherical triangle, the sum of the angles is greater than 180° and can be up to 540°. Specifically, the sum of the angles is where "f" is the fraction of the sphere's area which is enclosed by the triangle. Note that spherical geometry does not satisfy several of Euclid's axioms (including the parallel postulate.) 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