Question

which set of angle measures could be the measures of the interior angles of a triangle? 31°, 75°, and 70°; 100°, 48°, and 42°; 60°, 60°, and 60°; 90°, 42°, and 58°

Explanation:

Step1: Recall Triangle Angle Sum

The sum of interior angles of a triangle is \(180^\circ\). We'll check each set by adding their angles.

Step2: Check First Set

First set: \(31^\circ + 75^\circ + 70^\circ = 176^\circ
eq 180^\circ\). Not valid.

Step3: Check Second Set

Second set: \(100^\circ + 48^\circ + 42^\circ = 190^\circ
eq 180^\circ\). Not valid.

Step4: Check Third Set

Third set: \(60^\circ + 60^\circ + 60^\circ = 180^\circ\). Valid.

Step5: Check Fourth Set

Fourth set: \(90^\circ + 42^\circ + 58^\circ = 190^\circ
eq 180^\circ\). Not valid.

Answer:

The set \(60^\circ\), \(60^\circ\), and \(60^\circ\) (the third set)