Question

a triangle has angles that measure 65° and 75°. which is the measure of the third angle of the triangle? 30° 40° 50° 60°

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. Let the three angles be \(A\), \(B\), and \(C\). So \(A + B+C=180^{\circ}\). Given \(A = 65^{\circ}\) and \(B = 75^{\circ}\).

Step2: Solve for the third angle

We can find \(C\) by \(C=180^{\circ}-(A + B)\). Substitute \(A = 65^{\circ}\) and \(B = 75^{\circ}\) into the formula: \(C=180-(65 + 75)=180 - 140=40^{\circ}\).

Answer:

40°