Question

1. if a triangle has two angles that measure 46 and 102 degrees, what is the measure of the third angle? 44° 46° 56° 32°

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

Step2: Identify known angles

We know \(A = 46^{\circ}\) and \(B = 102^{\circ}\), and we want to find \(C\).

Step3: Calculate the third - angle

We can rewrite the angle - sum formula as \(C=180^{\circ}-A - B\). Substitute \(A = 46^{\circ}\) and \(B = 102^{\circ}\) into the formula: \(C=180^{\circ}-46^{\circ}-102^{\circ}=32^{\circ}\).

Answer:

D. 32°