How Many Acute Angles Does a Triangle Have?

many-acute-angles-triangle Credit: Milestoned/CC-BY 2.0

A triangle has either two or three acute angles, depending on the type of triangle. Right and obtuse triangles have two acute angles, whereas an acute triangle has three acute angles.

A triangle must be either acute, right, or obtuse. It also has three interior angles that always total 180 degrees. Because a right triangle has a right angle (exactly 90 degrees), the sum of its two remaining angles must be 90 degrees. These two angles are therefore inferred to be acute. The same holds true for an obtuse triangle, since it has an obtuse angle (measuring more than 90 degrees) that makes the sum of its two other angles be less than 90 degrees. No triangle has only one acute angle, or it wouldn't be a triangle.