Question

which set of angle measures could be the measures of the interior angles of a triangle?
60°, 45°, and 70°
30°, 85°, and 25°
55°, 90°, and 35°
110°, 15°, and 45°

Explanation:

Step1: Recall triangle angle sum

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

Step2: Check first option

\(60^\circ + 45^\circ + 70^\circ = 175^\circ
eq 180^\circ\), so not valid.

Step3: Check second option

\(30^\circ + 85^\circ + 25^\circ = 140^\circ
eq 180^\circ\), so not valid.

Step4: Check third option

\(55^\circ + 90^\circ + 35^\circ = 180^\circ\), which matches the triangle angle sum.

Step5: Check fourth option (optional, but for completeness)

\(110^\circ + 15^\circ + 45^\circ = 170^\circ
eq 180^\circ\), so not valid.

Answer:

\(55^\circ\), \(90^\circ\), and \(35^\circ\) (the third option)