Exterior Angle Inequality Theorem

Consider a triangle. Let ∠ A be an exterior angle of the triangle, and let ∠ B and ∠ C be the remote interior angles of ∠ A.

The measure of the exterior angle A is equal to the sum of the measures of its remote interior angles by the Triangle Exterior Angle Theorem. m∠ A = m∠ B + m∠ C In a triangle, every interior angle has positive measure. Then, the sum of the measures of the interior angles B and C is greater than the measure of ∠ B. Similarly, the sum of the measures of ∠ B and ∠ C is greater than the measure of ∠ C. m∠ B + m∠ C > m∠ B m∠ B + m∠ C > m∠ C Substituting m∠ A for m∠ B + m∠ C in each inequality, the required inequalities are obtained.