A triangle with exactly one angle measuring greater than 90 degrees falls under which category?

A triangle with exactly one angle measuring greater than 90 degrees is classified as an obtuse triangle. This classification is based on the definition of obtuse angles in geometry, where an obtuse angle is one that measures more than 90 degrees but less than 180 degrees.

In the case of an obtuse triangle, since there is only one angle that is obtuse, the other two angles must be acute (each measuring less than 90 degrees) to satisfy the triangle sum theorem, which states that the sum of the angles in any triangle must equal 180 degrees.

This characteristic specifically distinguishes obtuse triangles from other types, such as equilateral triangles (which have all three angles equal and each measuring 60 degrees), isosceles triangles (which can have two sides of equal length but can have angles measuring less than or equal to 90 degrees), and right triangles (which have one angle exactly equal to 90 degrees). Thus, the category of obtuse triangle is the accurate classification for a triangle with one angle greater than 90 degrees.