Question

the measures of two angles of a triangle are 66° and 62°. find the measure of the third angle.

Explanation:

Step1: Recall angle - sum property

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

Step2: Substitute known values

We know \(A = 66^{\circ}\) and \(B = 62^{\circ}\). Then \(C=180^{\circ}-(66^{\circ}+ 62^{\circ})\).

Step3: Calculate the third - angle

First, find the sum of the two given angles: \(66^{\circ}+62^{\circ}=128^{\circ}\). Then \(C = 180^{\circ}-128^{\circ}=52^{\circ}\).

Answer:

\(52^{\circ}\)