Skill: Classify triangles by angles

Look at the measures of the three interior angles of the triangle.

• 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 $90^\circ$.

A triangle’s angles always add to $180^\circ$, so it cannot have two right or obtuse angles.

Example

Classify a triangle with angles measuring $35^\circ$, $90^\circ$, and $55^\circ$.

1. Check that the angles make a triangle:

$$35^\circ+90^\circ+55^\circ=180^\circ$$

2. Look for an angle equal to $90^\circ$.

   The triangle has one angle measuring $90^\circ$.

3. Therefore, the triangle is a right triangle.

The triangle’s position, size, or side lengths do not change its classification; only its angle measures matter.