Question

the measures of two angles of a triangle are 98° and 20°. 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 \(A + B + C=180^{\circ}\). Given \(A = 98^{\circ}\) and \(B = 20^{\circ}\).

Step2: Solve for the third angle

We can find \(C\) by the formula \(C=180^{\circ}-A - B\). Substitute \(A = 98^{\circ}\) and \(B = 20^{\circ}\) into the formula: \(C=180^{\circ}-98^{\circ}-20^{\circ}\). First, \(180^{\circ}-98^{\circ}=82^{\circ}\), then \(82^{\circ}-20^{\circ}=62^{\circ}\).

Answer:

\(62^{\circ}\)