Identify Triangles by Angles

1) Know the three angle-based types

A triangle can be identified by its angles:

• Acute triangle: all three angles are less than 90°.
• Right triangle: one angle is exactly 90°.
• Obtuse triangle: one angle is greater than 90°.

2) Examine the given angles

Look at each angle carefully. You usually only need to find:

• whether any angle is 90°,
• whether any angle is greater than 90°,
• or whether all angles are below 90°.

If only two angles are shown, use the triangle angle sum idea: the angles in a triangle add to 180°. Find the missing angle by subtraction, then classify the triangle.

3) Decide the classification

Use this order:

1. If one angle is 90°, the triangle is right.
2. Else if one angle is greater than 90°, the triangle is obtuse.
3. Otherwise, it is acute.

4) Check your answer

Make sure your classification matches every angle given. If you found a missing angle, confirm that all three angles add to 180°. Then simplify your final response to just the correct triangle type.