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 ________ the sum of the measures of the ________ remote interior angle(s).

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: Solve for \(D\)

From \(C + D=180^{\circ}\), we have \(C = 180^{\circ}-D\). Substituting \(C\) into \(A + B + C=180^{\circ}\), we get \(A + B+(180^{\circ}-D)=180^{\circ}\). Simplifying gives \(A + B=D\). 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:

equal to