Classify triangles by angles

Triangles are classified by the measures of their three interior angles: acute triangles have three angles less than 90°, right triangles have one angle equal to 90°, and obtuse triangles have one angle greater than 90°. The classification is unchanged by a triangle’s orientation, size, or side lengths; recognizing that a triangle’s angles total 180° explains why it cannot have more than one right or obtuse angle and supports later reasoning about geometric angle relationships.

Detailed Explanation: 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 $55^\circ$ .

Check that the angles make a triangle:

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

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

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

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