Skill: Classify triangles by angle measures

Look at the angle measures, not the side lengths:

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

The angles in every triangle add to $180^\circ$.

Example: Classify a triangle with angles measuring $48^\circ$, $90^\circ$, and $42^\circ$.

1. Check that the angles form a triangle:

$$48^\circ+90^\circ+42^\circ=180^\circ$$

2. Look for an angle measuring $90^\circ$. The triangle has one angle of $90^\circ$.

3. Therefore, the triangle is a right triangle.

A triangle cannot have two right angles or two obtuse angles because their measures would already total at least $180^\circ$, leaving no angle measure for the third angle.