Question

acute obtuse right triangle a acute obtuse right triangle b acute obtuse right triangle c acute obtuse right triangle d

Explanation:

Step1: Recall triangle angle - type definitions

An acute triangle has all angles less than \(90^{\circ}\). An obtuse triangle has one angle greater than \(90^{\circ}\). A right - triangle has one angle equal to \(90^{\circ}\).

Step2: Analyze Triangle A

The angles are \(35^{\circ},120^{\circ},25^{\circ}\). Since \(120^{\circ}>90^{\circ}\), Triangle A is obtuse.

Step3: Analyze Triangle B

The angles are \(80^{\circ},50^{\circ},50^{\circ}\). All \(80^{\circ}<90^{\circ},50^{\circ}<90^{\circ}\), so Triangle B is acute.

Step4: Analyze Triangle C

The angles are \(75^{\circ},50^{\circ},55^{\circ}\). All \(75^{\circ}<90^{\circ},50^{\circ}<90^{\circ},55^{\circ}<90^{\circ}\), so Triangle C is acute.

Step5: Analyze Triangle D

There is a \(90^{\circ}\) angle (right - angle), so Triangle D is right.

Answer:

Triangle A: Obtuse; Triangle B: Acute; Triangle C: Acute; Triangle D: Right