Which type of triangle has exactly one angle greater than 90 degrees?

A triangle that has exactly one angle greater than 90 degrees is classified as an obtuse triangle. In geometry, an obtuse angle is defined as an angle that measures more than 90 degrees but less than 180 degrees. Therefore, in an obtuse triangle, one of the angles measures greater than 90 degrees, while the other two angles must be acute, meaning they each measure less than 90 degrees. This configuration maintains the fundamental property that the sum of the angles in any triangle must equal 180 degrees.

The other types of triangles do not meet this criterion. A right triangle has one angle that is exactly 90 degrees. An isosceles triangle can be further classified into types based on its angles, but it does not specifically indicate that one angle is greater than 90 degrees as a defining characteristic. An equilateral triangle has all three angles equal to 60 degrees, which is acute. Therefore, the definition of an obtuse triangle uniquely identifies it as having an angle exceeding 90 degrees, making it the correct answer.