Complementary vs. Supplementary Angles: What's the Difference?

In geometry, angles often come in pairs. Two of the most common—and often confused—relationships are Complementary and Supplementary angles. You'll see these terms constantly in math homework, engineering diagrams, and design.

The definitions are simple, but remembering which is which can be tricky. This guide will give you the definitions, visual examples, and a foolproof memory trick to never mix them up again.

Complementary Angles (The "Corner" Pair)

Two angles are complementary if their measurements add up to exactly 90 degrees.

• The Math: Angle A + Angle B = 90°
• The Visual: Together, they form a perfect Right Angle (an "L" shape).

Examples

• 30° and 60° are complementary (30 + 60 = 90).
• 45° and 45° are complementary.
• 1° and 89° are complementary.

Real-world analogy: Think of a picture frame corner. If you cut the wood at two angles to make that 90° corner, those two cuts must be complementary.

Supplementary Angles (The "Straight" Pair)

Two angles are supplementary if their measurements add up to exactly 180 degrees.

• The Math: Angle A + Angle B = 180°
• The Visual: Together, they form a Straight Line.

Examples

• 100° and 80° are supplementary (100 + 80 = 180).
• 90° and 90° are supplementary.
• 135° and 45° are supplementary.

Real-world analogy: Open a book until it lies flat on the table. The two pages form a straight line (180°). If you lift one page slightly, the angle it makes with the table plus the angle it makes with the other page still relates to that flat line.

The Memory Trick (Never Forget!)

How do you remember which is 90° and which is 180°? Use the "C" and "S" trick:

1. The "C" Trick

Complementary starts with C. You can turn the letter C into the number 9 (for 90) by drawing a line down.

• C -> Corner (90°)

2. The "S" Trick

Supplementary starts with S. You can turn the letter S into the number 8 (for 180) by connecting the ends.

• S -> Straight (180°)

Practice Problem

Let's test your knowledge.

Question: Angle A is 40°.

1. What is its complement?
2. What is its supplement?

Answer:

1. Complement: We need a total of 90°. 90° - 40° = 50°. So, the complement is 50°.

2. Supplement: We need a total of 180°. 180° - 40° = 140°. So, the supplement is 140°.

Why Does This Matter?

Architects and carpenters use these pairs every day.

• Flooring: When laying floor tiles in a diamond pattern, cuts must be complementary to fit in the room corners.
• Roads: Civil engineers calculate banking angles on roads using supplementary relationships to ensure cars don't slide off during turns.

Conclusion

• Complementary = Adds to 90° (Corner)
• Supplementary = Adds to 180° (Straight Line)

Next time you see a pair of angles, just ask yourself: "Do they make a corner or a line?"

Need to check an angle yourself? Use our free Online Protractor to measure any image instantly.