Classify triangles by angle measures

Classification by angle measures identifies a triangle as acute when all three angles are less than $90^\circ$ , right when exactly one angle measures $90^\circ$ , or obtuse when exactly one angle is greater than $90^\circ$ . This reasoning relies on the triangle angle-sum relationship of $180^\circ$ , which rules out multiple right or obtuse angles and distinguishes angle-based classification from classification by side lengths.

Detailed Explanation: 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 $42^\circ$ .

Check that the angles form a triangle:

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

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

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Triangle Classification - Angles

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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

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Triangle Classification - Angles