Acute and obtuse triangles Acute and obtuse triangles An acute triangle is a triangle with all three angles acute (less than 90°). An obtuse triangle is one with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180°, no triangle can have more than one obtuse angle. Acute and obtuse triangles are the two different types of oblique triangles—triangles that are not right triangles because they have no 90° angle. In all triangles, the centroid—the intersection of the medians, each of which connects a vertex with the midpoint of the opposite side—and the incenter—the center of
Angular defect to less than 360°, on a spherical triangle the interior angles always add up to more than 180° (the exterior angles add up to "less" than 360°), and the angles in a hyperbolic triangle always add up to less than 180° (the exterior angles add up to "more" than 360°). In modern terms, the defect at a vertex or over a triangle (with a minus) is precisely the curvature at that point or the total (integrated) over the triangle, as established by the Gauss–Bonnet theorem. For a polyhedron, the defect at a vertex equals 2π minus the sum of all