A triangle cannot have two obtuse angles because it would violate the fundamental property of triangles, which states that the sum of all interior angles must equal 180°. An obtuse angle is any angle greater than 90°, and if a triangle had two such angles, their combined total would exceed 180°, leaving no room for the third angle. This makes it geometrically impossible for a triangle to have more than one obtuse angle.
Triangles can only have one obtuse angle (as in an obtuse triangle) or no obtuse angles, but never two or more.