Question

problem 6: (first taught in lesson 31) complete this sentence with the best of the choices given. the measure of an exterior angle of a triangle is equal to the ____ of the measures of the two ____ interior angles. a b c d e difference; remote

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 \(C\). Then \(A + B + C=180^{\circ}\) and \(C + D = 180^{\circ}\).

Step2: Derive the exterior - angle property

From \(A + B + C=180^{\circ}\) and \(C + D = 180^{\circ}\), we can set \(A + B + C=C + D\). Subtracting \(C\) from both sides of the equation \(A + B + C=C + D\) gives \(A + B=D\), where \(A\) and \(B\) are the remote interior angles with respect to the exterior angle \(D\).

Answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. So the correct option is not shown among A - E as presented, but the correct words are "sum; remote".