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Triangle Classification by Angles

Angle relationships and examples for accurate classification.

By Geometry Editorial Team | 2026-06-02

Quick Answer

Angle-based classification uses the largest interior angle to identify acute, right, or obtuse triangles.

A + B + C = 180 degrees

Table of Contents

Introduction

Start from the Classifying Triangles Calculator homepage if you want to test angle sets and see the third angle computed instantly.

Angle classification is essential for identifying right triangles and understanding geometry behavior in practical problems.

Main Content

What is it?

The angle class is based on whether the largest angle is less than, equal to, or greater than 90.

To compare with side rules, review Triangle Classification by Sides. To avoid invalid inputs, revisit Triangle Inequality Theorem when side values are also involved.

Formula

When two angles are known, compute the third by subtraction from 180.

Then classify using the largest angle threshold rule.

Step-by-step guide

  1. Validate all angles are positive.
  2. Ensure total is exactly 180 degrees.
  3. Find the largest angle value.
  4. Assign acute, right, or obtuse.

Example

Angles 40, 60, and 80 produce an acute triangle. Angles 30, 60, and 90 produce a right triangle.

FAQ

Can a triangle have two right angles?

No, that would exceed the 180-degree total.

Is angle classification enough by itself?

For angle class yes, but side class needs side data.

Conclusion

Angle-based classification is fast and reliable when angle sum validation is done first.

Try angle inputs

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