What is an obtuse triangle?

What is an obtuse triangle?

• A. A triangle with three acute angles.
• B. A triangle with a right angle.
• C. A triangle with one obtuse angle.
• D. A triangle with all angles equal.

Answer: (C)

An obtuse triangle has exactly one angle greater than 90 degrees. The interior angles in any triangle sum to 180 degrees, so if one angle is obtuse, the other two must be acute and add up to less than 90 degrees. You can’t have two obtuse angles in a triangle, because that would already exceed 180. So the defining feature is a single angle that is greater than 90 degrees. The other descriptions refer to different triangle types: three acute angles make an acute triangle, a right angle makes a right triangle, and all angles equal describes an equiangular/equilateral triangle with 60-degree angles.

An obtuse triangle has exactly one angle greater than 90 degrees. The interior angles in any triangle sum to 180 degrees, so if one angle is obtuse, the other two must be acute and add up to less than 90 degrees. You can’t have two obtuse angles in a triangle, because that would already exceed 180. So the defining feature is a single angle that is greater than 90 degrees. The other descriptions refer to different triangle types: three acute angles make an acute triangle, a right angle makes a right triangle, and all angles equal describes an equiangular/equilateral triangle with 60-degree angles.