Graduate Management Admission Test (GMAT) Practice Test

According to the exterior angle theorem, what does the exterior angle at a vertex of a triangle equal?

1. The sum of the lengths of the sides

2. The sum of the sizes of the interior angles at the other two vertices

3. The difference between the largest and smallest angles

4. The average of the interior angles

The correct answer is: The sum of the sizes of the interior angles at the other two vertices

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the interior angles opposite to it. This principle can be visualized by extending one side of the triangle to form an exterior angle. By doing so, the newly formed angle consists of two interior angles from the triangle, and their combined measure will equal the measure of the exterior angle. For example, in a triangle with vertices A, B, and C, if you extend the line segment AC to form an exterior angle at vertex A, that exterior angle will equal the sum of the angles at vertices B and C. This theorem is helpful in solving various geometric problems because it provides a direct relationship between the interior and exterior angles of a triangle, enabling one to find missing angle measures easily. Other options provide incorrect or unrelated interpretations of angle relationships in triangles. Understanding the correct application of the exterior angle theorem is essential for solving related geometry problems effectively.