Skill: 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.