Question

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

Explanation:

Step1: Recall triangle angle sum

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

Step2: Check first set (\(55^\circ, 90^\circ, 35^\circ\))

Sum: \(55 + 90 + 35 = 180^\circ\).

Step3: Check second set (\(60^\circ, 45^\circ, 70^\circ\))

Sum: \(60 + 45 + 70 = 175^\circ
eq 180^\circ\).

Step4: Check third set (\(110^\circ, 15^\circ, 45^\circ\))

Sum: \(110 + 15 + 45 = 170^\circ
eq 180^\circ\).

Step5: Check fourth set (\(30^\circ, 85^\circ, 25^\circ\))

Sum: \(30 + 85 + 25 = 140^\circ
eq 180^\circ\).

Answer:

The set \(55^\circ\), \(90^\circ\), and \(35^\circ\) (the first set)