Question

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

44°
46°
32°
56°

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A = 46^{\circ}\), \(B=102^{\circ}\), and \(C\) (the unknown angle). Then \(A + B + C=180^{\circ}\).

Step2: Solve for the unknown angle \(C\)

Substitute the values of \(A\) and \(B\) into the equation: \(C = 180^{\circ}-(A + B)\).

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Answer:

\(32^{\circ}\) (the third - option)