Definition:

An obtuse triangle is a triangle that has one angle measuring more than 90 degrees. This means that the sum of the other two angles is less than 90 degrees.

Properties of an Obtuse Triangle:

• It has one angle greater than 90 degrees.
• It can never be a right triangle (a triangle with one 90-degree angle).
• The sum of all angles in an obtuse triangle is always 180 degrees.
• The side opposite the obtuse angle is the longest side in the triangle.

Example:

For example, in a triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees, the triangle is not obtuse because it does not have an angle greater than 90 degrees. However, in a triangle with angles measuring 30 degrees, 60 degrees, and 100 degrees, the triangle is obtuse because it has one angle greater than 90 degrees (100 degrees).

Practice Problem:

Find the type of triangle and the measure of the unknown angle:
Angle A = 45 degrees, Angle B = 60 degrees, Angle C = ___ degrees

Angle C = 180 - (45 + 60) = 180 - 105 = 75 degrees