Which of the following triangles can have one angle greater than 90 degrees?

Which of the following triangles can have one angle greater than 90 degrees?

• A. Right triangle
• B. Acute triangle
• C. Obtuse triangle
• D. Equilateral triangle

Answer: (C)

A triangle can have one angle greater than 90 degrees if it is classified as an obtuse triangle. In an obtuse triangle, by definition, one of the angles measures greater than 90 degrees while the other two angles must be acute, meaning each is less than 90 degrees. This characteristic allows the sum of all angles in the triangle to still equal 180 degrees. In contrast, a right triangle contains one angle exactly equal to 90 degrees, while an acute triangle is defined by having all three angles less than 90 degrees. An equilateral triangle has all three angles equal to each other, specifically 60 degrees each, which also does not allow for any angle to exceed 90 degrees. Thus, the only type of triangle that can accommodate an angle greater than 90 degrees is the obtuse triangle.

A triangle can have one angle greater than 90 degrees if it is classified as an obtuse triangle. In an obtuse triangle, by definition, one of the angles measures greater than 90 degrees while the other two angles must be acute, meaning each is less than 90 degrees. This characteristic allows the sum of all angles in the triangle to still equal 180 degrees.

In contrast, a right triangle contains one angle exactly equal to 90 degrees, while an acute triangle is defined by having all three angles less than 90 degrees. An equilateral triangle has all three angles equal to each other, specifically 60 degrees each, which also does not allow for any angle to exceed 90 degrees. Thus, the only type of triangle that can accommodate an angle greater than 90 degrees is the obtuse triangle.