Exterior Angle Theorem Math Definition

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Exterior angle theorem math definition. The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles. The exterior angle theorem the exterior angle theorem says that if you add the measures of the two remote interior angles you get the measure of the exterior angle. The exterior angle theorem tells us that the measure of angle d is equal to the sum of angles a and b. An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

In the figure above drag the orange dots on any vertex to reshape the triangle. This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate. In several high school treatments of geometry the term exterior angle theorem has been applied to a different result namely the portion of proposition 1 32 which states that the m. The interior angles of a triangle add up to 180 show step by step solutions.

The exterior angle theorem is proposition 1 16 in euclid s elements which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles. Here we see that 120 80 40. The angles on a straight line add up to 180 2. The exterior angle d is greater than angle a or angle b.

We can derive the exterior angle theorem using the information that 1. The exterior angle d equals the angles a plus b. This theorem is a shortcut you can use to find an exterior angle.