Classify triangles by angle measures

Triangles are classified by their angle measures as acute (three angles less than $90^\circ$ ), right (one $90^\circ$ angle), or obtuse (one angle greater than $90^\circ$ ). This classification relies on the triangle angle-sum relationship of $180^\circ$ , which means a triangle cannot have more than one right or obtuse angle, and distinguishes angle-based categories from classifications based on side lengths.

Detailed Explanation: Classify triangles by angle measures

To classify a triangle by its angle measures, look at the sizes of its three angles:

Acute triangle: all three angles are less than $(90^\circ)$ .
Right triangle: one angle is exactly $(90^\circ)$ .
Obtuse triangle: one angle is greater than $(90^\circ)$ .

The angles in every triangle add to $(180^\circ)$ . This helps you find a missing angle and check your answer.

Example: A triangle has angles measuring $(48^\circ)$ and $(67^\circ)$ . Classify the triangle.

Step 1: Find the missing angle.

48^\circ+67^\circ=115^\circ

Subtract from $(180^\circ)$ :

180^\circ-115^\circ=65^\circ

The three angles are $(48^\circ)$ , $(67^\circ)$ , and $(65^\circ)$ .

Step 2: Compare each angle with $(90^\circ)$ .

48^\circ<90^\circ,\qquad 67^\circ<90^\circ,\qquad 65^\circ<90^\circ

All three angles are less than $(90^\circ)$ , so the triangle is an acute triangle.

Remember, this classification uses angle measures, not side lengths.

Learn by doing: Classify triangles by angle measures

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Triangle Classification - Angles

Earned ?

Classify triangles by angle measures

Detailed Explanation: Classify triangles by angle measures

Learn by doing: Classify triangles by angle measures

Practice with unlimited practice problems

Practice:

Triangle Classification - Angles