Supplementary Angles: Definition, Examples, Chart, and Practice

What are supplementary angles?

Supplementary angles are two angles that add up to exactly 180°.

A 180° angle is a straight angle in the types of angles chart. So, when two supplementary angles are placed side by side, they can make one straight line.

The angles do not have to be the same size. One angle can be small and the other can be large, as long as the total is 180°.

Supplementary angles rule

Use this rule every time you check or find supplementary angles.

Angle A + Angle B = 180°

For example, 120° and 60° are supplementary because 120° + 60° = 180°.

Supplementary angles chart

The chart shows pairs of angles that add to 180°.

A supplementary pair can include an acute angle, a right angle, or an obtuse angle. The total is what matters.

How to find a missing supplementary angle

If you know one angle, subtract it from 180°.

Missing angle = 180° - angle you know

This works because the two angles must make a straight angle total.

Worked example

Problem: One angle is 68°. What angle is supplementary to it?

Step 1: Write the rule: 68° + missing angle = 180°.

Step 2: Subtract from 180°: 180° - 68° = 112°.

Step 3: Check: 68° + 112° = 180°.

The supplementary angle is 112°.

Do supplementary angles have to touch?

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

If they touch and make a straight line, they are still supplementary.

If they are separate angles on the page, they are also supplementary as long as their measures add to 180°.

Supplementary angles and a straight line

When two touching angles sit on a straight line, they are called a linear pair.

A linear pair always makes 180°, so the two angles are supplementary.

This is why straight-line diagrams are helpful: if one angle is given, the angle beside it can be found by subtracting from 180°.

Supplementary vs. complementary angles

Supplementary and complementary sound alike, but one makes a straight angle and the other makes a right angle.

Supplementary angles add to 180° and can make a straight angle.

Complementary angles add to 90° and can make a right angle.

A helpful memory clue is this: supplementary is the bigger total, because 180° is bigger than 90°.

Real-life supplementary angle examples

A straight road with a side street can show two angles on a straight line.

A ruler edge with one ray drawn from a point can split the straight line into two supplementary angles.

A door opened wide can make one angle with a wall, while the rest of the straight line makes the angle that completes 180°.

Common mistakes

Do not call angles supplementary just because they touch. They must add to 180°.

Do not confuse supplementary with complementary. Supplementary totals 180°, while complementary totals 90°.

Do not forget that one supplementary angle can be obtuse and the other can be acute. In crossed-line diagrams, the angle beside a vertical angle often uses this same 180° total.

Check subtraction carefully. The supplement of 47° is 133°, because 180° - 47° = 133°.

Quick practice

1. Are 80° and 100° supplementary? Yes, because 80° + 100° = 180°.

2. Find the supplement of 35°. The answer is 145° because 180° - 35° = 145°.

3. Are 90° and 90° supplementary? Yes, because they add to 180°.

4. Are 70° and 90° supplementary? No, because 70° + 90° = 160°.

5. If x and 118° are supplementary, x = 62° because 180° - 118° = 62°.