Why Can't a Triangle Have More Than One Obtuse Angle?

Why Can't a Triangle Have More Than One Obtuse Angle?

Why Can't a Triangle Have More Than One Obtuse Angle?

An obtuse angle is more than 90 degrees. The three angles within any triangle always equal exactly 180 degrees. If two angles are obtuse — even if they are both only 91 degrees — they add up to more than 180 degrees. Therefore, it is impossible for more than one angle in a triangle to be greater than 90 degrees.

A triangle with one angle greater than 90 degrees is an obtuse triangle. There are other names for triangles that are based, at least in part, on their angles. For instance, a right triangle has one right angle, which is 90 degrees. The degrees of the other two angles add up to 90, for a total of 180 degrees.

An equilateral triangle has three equal angles as well as three equal sides. The measurement of each angle is 60 degrees, though the lengths of the sides vary from triangle to triangle. In an isosceles triangle, two of the angles have identical degrees, and each must be less than 90 degrees. In addition, two of the sides are the same length. An acute triangle has three acute angles, or angles that are less than 90 degrees. A scalene triangle, however, is described only by its noncongruent sides, or sides of different lengths.