Question

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

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation

Let the third angle be \(x\). Then \(x + 46^{\circ}+ 102^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x=180^{\circ}-(46^{\circ}+ 102^{\circ})\)
\(x = 180^{\circ}-148^{\circ}\)
\(x = 32^{\circ}\)

Answer:

\(32^{\circ}\) (the first option)