Question

problem 6: complete this sentence with the best of the choices given. the measure of an exterior angle of a triangle is ____ the sum of the measures of the ____ remote interior angles. a. equal to; largest b. supplementary to; largest c. complementary to; two d. complementary to; smallest e. equal to; two

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180 degrees. Let the triangle have interior angles \(A\), \(B\), and \(C\), and an exterior angle \(D\) adjacent to \(C\). So \(A + B + C=180^{\circ}\), and \(C + D = 180^{\circ}\).

Step2: Derive exterior - angle relationship

From \(A + B + C=180^{\circ}\) and \(C + D = 180^{\circ}\), we can subtract \(C\) from both equations. We get \(A + B=D\). So the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Answer:

E. equal to; two