Question

which diagram shows possible angle measures of a triangle? diagram 1: triangle with angles 35°, 120°, 35° diagram 2: triangle with angles 32°, 115°, 33° diagram 3: triangle with angles 35°, 115°, 25° diagram 4: triangle with angles 35°, 120°, 30°

Explanation:

Step1: Recall triangle angle sum

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

Step2: Check first diagram

Angles: \(35^\circ\), \(120^\circ\), \(35^\circ\). Sum: \(35 + 120 + 35 = 190^\circ\). Not \(180^\circ\), invalid.

Step3: Check second diagram

Angles: \(32^\circ\), \(115^\circ\), \(33^\circ\). Sum: \(32 + 115 + 33 = 180^\circ\). Valid.

Step4: Check third diagram

Angles: \(35^\circ\), \(115^\circ\), \(25^\circ\). Sum: \(35 + 115 + 25 = 175^\circ\). Not \(180^\circ\), invalid.

Step5: Check fourth diagram

Angles: \(35^\circ\), \(120^\circ\), \(30^\circ\) (assuming the last angle is \(30^\circ\)). Sum: \(35 + 120 + 30 = 185^\circ\). Not \(180^\circ\), invalid.

Answer:

The second diagram (with angles \(32^\circ\), \(115^\circ\), \(33^\circ\))