Angles in a Triangle: Definition, Rule, Examples, Chart, and Practice

What are angles in a triangle?

A triangle has three inside angles.

These angles are called interior angles because they are inside the triangle.

No matter what the triangle looks like, the three interior angles always add to the same total.

Triangle angle rule

Use this rule for every triangle.

Angle A + Angle B + Angle C = 180°

This means the three inside angles of a triangle make a straight angle when placed together.

Triangle angle chart

The 180° rule works for every type of triangle.

A triangle may use names from types of angles, such as acute, right, or obtuse, and side names such as scalene, isosceles, or equilateral.

A triangle with one right angle still follows the same 180° rule.

How to find a missing triangle angle

Step 1: Add the two angles you know.

Step 2: Subtract that total from 180°.

Step 3: The answer is the missing inside angle.

For more worked problems and an answer-checking tool, use the focused lesson on finding the missing angle of a triangle.

Worked example

Problem: A triangle has angles of 48° and 72°. What is the missing angle?

Step 1: Add the known angles: 48° + 72° = 120°.

Step 2: Subtract from 180°: 180° - 120° = 60°.

Answer: The missing angle is 60°.

Triangle angles with algebra

Sometimes one triangle angle is written as an expression.

Example: the angles are x, 64°, and 81°.

Write x + 64 + 81 = 180. Then x + 145 = 180, so x = 35.

Why the rule works

If you cut off or copy the three corners of a triangle and place them side by side, they make a straight angle.

A straight angle is 180°.

That is why the three interior angles of a triangle always add to 180°.

This fact is also useful later in Angle-Angle-Side (AAS), because two known triangle angles force the third angle.

Common mistakes

Do not add to 360°. That is for a full turn, not the inside angles of one triangle.

Do not forget to subtract from 180° after adding the known angles.

Do not use an outside angle unless the problem asks for an exterior angle.

Quick practice

1. If two triangle angles are 40° and 70°, the missing angle is 70°.

2. If two triangle angles are 90° and 35°, the missing angle is 55°.

3. If the angles are x, 50°, and 60°, then x = 70°.

4. The three inside angles of every triangle add to 180°.