Question

classify the triangle by its angles.

Explanation:

Step1: Recall angle - based triangle classification

A triangle can be classified as acute, right, or obtuse based on its angles. An acute triangle has all angles less than \(90^{\circ}\), a right triangle has one angle equal to \(90^{\circ}\), and an obtuse triangle has one angle greater than \(90^{\circ}\).

Step2: Check each angle of the given triangle

The angles of the triangle are \(42^{\circ}\), \(64^{\circ}\), and \(74^{\circ}\). We check if each angle is less than \(90^{\circ}\).

• \(42^{\circ}<90^{\circ}\)
• \(64^{\circ}<90^{\circ}\)
• \(74^{\circ}<90^{\circ}\)

Since all three angles are less than \(90^{\circ}\), the triangle is an acute triangle.

Answer:

Acute triangle