Find the Missing Angle of a Triangle: Steps, Examples, and Practice

What does missing angle mean?

A missing angle is an angle measure that is not written in the diagram yet.

In a triangle, you can often find the missing angle when you know the other two inside angles.

This works because every triangle has three interior angles, and those three angles always add to 180°. Review angles in a triangle first if you want the full rule explanation.

The missing angle rule

Use this rule when two inside angles of a triangle are known.

Missing angle = 180° - first known angle - second known angle

You can also add the known angles first, then subtract once. Both methods give the same answer.

How to find the missing angle

Step 1: Check that the angles are inside the triangle.

Step 2: Add the two angle measures you already know.

Step 3: Subtract that sum from 180°.

Step 4: Write the answer with the degree symbol. The answer is an angle measure, so use °.

Basic examples

Example 1: 40° and 70° are known. 40° + 70° = 110°, so the missing angle is 180° - 110° = 70°.

Example 2: 52° and 68° are known. 52° + 68° = 120°, so the missing angle is 180° - 120° = 60°.

Example 3: 33° and 89° are known. 33° + 89° = 122°, so the missing angle is 180° - 122° = 58°.

Example chart

This chart shows several common missing-angle setups.

The same idea is used every time: add what you know, then subtract from 180°.

Right triangle examples

A right triangle already has one 90° angle.

So the two smaller acute angles must add to 90°.

Example: A right triangle has one acute angle of 37°. The other acute angle is 90° - 37° = 53°. This is a focused use of the right angle idea.

Isosceles triangle examples

An isosceles triangle has two equal sides, and the angles opposite those equal sides are also equal.

Example 1: If the two equal base angles are 48° and 48°, the top angle is 180° - 96° = 84°.

Example 2: If the top angle is 40°, the two equal base angles share 140°. Each base angle is 140° ÷ 2 = 70°.

Algebra examples

Sometimes the missing angle is written with a letter such as x.

Example 1: The angles are x, 64°, and 81°. Write x + 64 + 81 = 180. Then x + 145 = 180, so x = 35.

Example 2: The angles are 2x, 50°, and 70°. Write 2x + 50 + 70 = 180. Then 2x + 120 = 180, so 2x = 60 and x = 30. The missing angle 2x is 60°.

Exterior angle examples

Sometimes the diagram shows an outside angle beside the triangle.

If the outside angle and the inside angle sit on a straight line, they are supplementary, so they add to 180°.

Example: If the outside angle is 125°, the inside angle beside it is 180° - 125° = 55°. Then use the triangle rule to find any remaining angle.

Check if your answer makes sense

After you find the missing angle, add all three inside angles to check your work.

If the total is 180°, your calculation fits the triangle rule.

If the answer is negative or 0°, the given angles cannot make a normal triangle. If one inside angle is more than 90°, the triangle is an obtuse triangle.

Why this matters later

Missing-angle work is used in proofs, transformations, and triangle congruence.

For example, the triangle congruence rule AAS depends on the fact that two known triangle angles force the third angle.

So this skill is not just arithmetic; it helps you read geometric diagrams correctly.

Quick practice

1. 30° and 80° are known. The missing angle is 70°.

2. 90° and 42° are known. The missing angle is 48°.

3. 111° and 29° are known. The missing angle is 40°.

4. In an isosceles triangle, the top angle is 46°. Each equal base angle is 67°.

5. The angles are x, 58°, and 77°. x = 45.