What Is an Obtuse Triangle?

Which of the following pairs of measures can be the measures of two angles of an obtuse triangle?

Incorrect. Since the sum of the measures of the angles of a triangle must be 180 degrees, the measure of the third angle of this triangle would be 180° - 40° - 60° = 80°. Since neither of these angles measure above 90 degrees, the triangle is not obtuse.

Incorrect. Because the sum of the measures of the angles of a triangle must be 180 degrees, the measure of the third angle of this triangle would be 180° - 90° - 45° = 45°. Since neither 45 degrees nor 90 degrees measure above 90 degrees, the triangle is not obtuse.

Excellent! Since a 100-degree angle is an obtuse angle, an obtuse triangle is formed. The sum of the measures of the angles of a triangle must be 180 degrees, so the third angle measures 180° - 100° - 60° = 20°, which is possible for an obtuse triangle.

In summary: [[summary]]

Triangles can be categorized by the measures of their angles. For example, a triangle with an angle measuring above 90 degrees has an obtuse angle. Therefore, it is called an __obtuse triangle__.

Note that the sum of the angles of a triangle must be 180 degrees, and a triangle must have three angles, so no more than one angle of a triangle can be obtuse. In an obtuse triangle the height may be found outside the triangle, so that it is perpendicular to the extension of the side. 

40° and 60°

45° and 90°

60° and 100°

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