Complementary Angles: Definition, Examples, Chart, and Practice

What are complementary angles?

Complementary angles are two angles that add up to exactly 90°. A 90° angle is a right angle.

When two complementary angles are put together, they can make one right angle.

The word complementary tells us the total. The angles can look different, but if the two numbers add to 90°, they are complementary.

Complementary angles rule

Use this rule to check or find complementary angles.

Angle A + Angle B = 90°

If one angle is 35° and the other angle is 55°, then 35° + 55° = 90°. That means the two angles are complementary.

Complementary angles chart

The chart shows common complementary angle pairs. Each row adds to 90°.

Most pairs use two acute angles. Acute means less than 90°, as shown in the types of angles chart. The pair 45° and 45° has two equal angles.

How to find a missing complementary angle

If you know one angle, subtract it from 90° to find the missing angle.

Missing angle = 90° - angle you know

This works because the two angles must fill one right angle.

Worked example

Problem: One angle is 28°. What angle completes it to 90°?

Step 1: Write the complementary angle rule: 28° + missing angle = 90°.

Step 2: Subtract the known angle from 90°: 90° - 28° = 62°.

Step 3: Check the answer: 28° + 62° = 90°.

The complementary angle is 62°.

Do complementary angles have to touch?

No. Complementary angles can touch, but they do not have to touch.

Touching complementary angles share a corner and one side. They sit beside each other and make a right angle.

Separate complementary angles do not touch, but they still add to 90°. For example, a 25° angle and a 65° angle are complementary because 25° + 65° = 90°.

How to identify complementary angles in a diagram

First, look for a right angle marker. A small square in the corner means the full angle is 90°.

Next, see if the right angle is split into two smaller angles. If the two smaller angles fill the right angle, they are complementary.

If the diagram gives only numbers, add the two angle numbers. If the sum is 90°, the angles are complementary.

Complementary vs. supplementary angles

Complementary angles make a right angle, while supplementary angles make a straight angle.

Complementary angles add to 90°. If they are next to each other, they make a right angle.

Supplementary angles add to 180°. If they are next to each other, they make a straight angle.

Algebra example with complementary angles

Sometimes a missing angle is shown with a letter, such as x.

Example: angles x and 41° are complementary. That means x + 41° = 90°.

Take away 41° from 90°: x = 90° - 41° = 49°. So x = 49°.

Real-life complementary angle examples

The corner of a book is a right angle. If you draw one line from the corner, it can split the right angle into two complementary angles.

A wall and floor meet at 90°. A ramp inside that corner can make two smaller angles that add to 90°.

A clock can also show a right angle. If that right angle is split into two parts, the two parts are complementary.

Common mistakes

Do not call angles complementary just because they are next to each other. They must add to 90°.

Do not confuse complementary with supplementary. Complementary totals 90°, while supplementary angles total 180°.

Do not use 90° with another angle and call them complementary. If one angle is already 90°, there is no room left.

Check your subtraction carefully: the angle that completes 64° is 26°, not 36°, because 90° - 64° = 26°.

Quick practice

1. Is 30° complementary to 60°? Yes, because 30° + 60° = 90°.

2. Find the complement of 72°. The answer is 18° because 90° - 72° = 18°.

3. Are 44° and 45° complementary? No, because 44° + 45° = 89°.

4. If x and 37° are complementary, x = 53° because 90° - 37° = 53°.