What is an obtuse triangle?

What is an obtuse triangle?

• A. A triangle with all angles less than 90 degrees
• B. A triangle with one angle equal to 90 degrees
• C. A triangle with one angle that is greater than 90 degrees
• D. A triangle with all equal sides

Answer: (C)

An obtuse triangle is defined by having one angle that measures greater than 90 degrees. This characteristic is distinct because in any triangle, the sum of the three interior angles must equal 180 degrees. When one angle exceeds 90 degrees, the remaining two angles must necessarily be acute (each less than 90 degrees) to satisfy the total of 180 degrees. This setup creates a unique shape that differentiates an obtuse triangle from other types of triangles, such as acute triangles, where all angles are less than 90 degrees, and right triangles, which contain exactly one 90-degree angle. Understanding these properties helps in identifying and categorizing triangles based on their angle measures.

An obtuse triangle is defined by having one angle that measures greater than 90 degrees. This characteristic is distinct because in any triangle, the sum of the three interior angles must equal 180 degrees. When one angle exceeds 90 degrees, the remaining two angles must necessarily be acute (each less than 90 degrees) to satisfy the total of 180 degrees. This setup creates a unique shape that differentiates an obtuse triangle from other types of triangles, such as acute triangles, where all angles are less than 90 degrees, and right triangles, which contain exactly one 90-degree angle. Understanding these properties helps in identifying and categorizing triangles based on their angle measures.