Which statement describes an obtuse triangle?

Which statement describes an obtuse triangle?

• A. All angles less than 90 degrees.
• B. Two obtuse angles.
• C. All sides equal.
• D. Exactly one angle is greater than 90 degrees.

Answer: (D)

An obtuse triangle is defined by having one angle that is greater than 90 degrees. If one angle is over 90, the other two angles must add up to less than 90, so neither of them can exceed 90, and you can’t have more than one obtuse angle. That makes exactly one angle greater than 90 the correct description. The other ideas describe different triangles: all angles less than 90 would be an acute triangle; having two obtuse angles isn’t possible in a flat triangle because the total angle sum would exceed 180 degrees; all sides equal describes an equilateral triangle, where all angles are 60 degrees and hence not obtuse.

An obtuse triangle is defined by having one angle that is greater than 90 degrees. If one angle is over 90, the other two angles must add up to less than 90, so neither of them can exceed 90, and you can’t have more than one obtuse angle. That makes exactly one angle greater than 90 the correct description.

The other ideas describe different triangles: all angles less than 90 would be an acute triangle; having two obtuse angles isn’t possible in a flat triangle because the total angle sum would exceed 180 degrees; all sides equal describes an equilateral triangle, where all angles are 60 degrees and hence not obtuse.