Supplementary Angles Calculator - Find the Missing Angle
Enter any angle between 0° and 180° and instantly find its supplementary angle — the one that, when added together, equals exactly 180°.
Two angles are supplementary when their sum is 180°. Enter angle A and the calculator returns angle B = 180° − A.
Supplementary Angles Calculator - Find the Missing Angle
Enter any angle between 0° and 180° and instantly find its supplementary angle — the one that, when added together, equals exactly 180°.
Enter a value between 0° and 180° (exclusive).
About the supplementary angles calculator
Two angles are called supplementary when their measures add up to exactly 180 degrees. If angle A measures 60°, then its supplement angle B measures 120°, because 60 + 120 = 180. The supplementary angles calculator automates this trivially simple but constantly needed subtraction so you never have to reach for pencil and paper.
Supplementary angles appear throughout geometry, trigonometry, architecture, and everyday practical tasks. In a triangle, the interior angle and the exterior angle at any vertex are always supplementary — they form a straight line. When a transversal crosses two parallel lines, co-interior angles (also called consecutive interior angles or same-side interior angles) are supplementary. This property is used constantly in proofs involving parallel lines.
In construction and design, supplementary angles arise whenever two surfaces meet to form a straight edge. If one side of a joint cuts at 35°, the mating piece must be cut at 145° so the two pieces lie flat together. Cabinet makers, metalworkers, tile setters, and frame builders all use supplementary angle relationships daily without necessarily calling them by that name.
It is important to distinguish supplementary angles from complementary angles. Complementary angles sum to 90°, not 180°. A common memory trick: the letter C in Complementary comes before S in Supplementary, just as 90 comes before 180. Supplementary angles also differ from a linear pair, though a linear pair is always supplementary — a linear pair specifically requires the two angles to be adjacent and to share a common ray, forming a straight line.
Supplementary angles do not need to be adjacent. Two non-adjacent angles are called supplementary if their measures add to 180°, and they can appear anywhere in a figure as long as the sum holds. For example, in a regular hexagon, any two non-adjacent interior angles whose positions are directly across from each other are supplementary to the angles that fill the gap between them in various configurations.
The formula is simply B = 180° − A. Enter your known angle in degrees, and the calculator returns the supplement immediately. You can also enter decimal angles such as 45.5° or 123.75° — the formula works equally well for any value strictly between 0° and 180°. Angles of exactly 0° or 180° are degenerate cases that do not form meaningful supplementary pairs, so the calculator restricts input to that open interval.
Supplementary angles examples
Four common scenarios showing the supplementary angle for different input angles.
| Angle A | Supplement B | Explanation |
|---|---|---|
| 30° | 150° | 30° is an acute angle. Its supplement is 150°, an obtuse angle. Together they form a straight line: 30 + 150 = 180. |
| 120° | 60° | 120° is an obtuse angle. Its supplement is 60°, an acute angle. 120 + 60 = 180. |
| 90° | 90° | A right angle is its own supplement — 90 + 90 = 180. Two perpendicular rays form exactly a straight line. |
| 45.5° | 134.5° | Decimal angles work perfectly. 45.5 + 134.5 = 180. Useful for precision woodworking and drafting. |
How to use the supplementary angles calculator
- Enter your known angle in the Angle (A)° field. The value must be between 0° and 180° exclusive.
- Click Calculate. The supplementary angle B appears instantly in the result panel, alongside the confirmation that A + B = 180°.
- Use the example buttons to instantly load a pre-set angle value and see the result.
- Click Reset to clear the field and enter a new angle.
Supplementary angles FAQ
What are supplementary angles?
Supplementary angles are two angles whose measures add up to exactly 180 degrees. For any angle A between 0° and 180°, the supplement is B = 180° − A. The two angles do not need to be adjacent; they only need to sum to 180°.
What is the difference between supplementary and complementary angles?
Complementary angles sum to 90°, while supplementary angles sum to 180°. A memory aid: Complementary (C comes before S) goes with 90°, and Supplementary goes with 180°. For example, the complement of 30° is 60°, but the supplement of 30° is 150°.
Can supplementary angles be equal to each other?
Yes. When both angles equal 90°, they are supplementary and equal. This is the only case where two supplementary angles are congruent, because 90 + 90 = 180 and no other pair of equal values sums to 180.
Do supplementary angles have to be adjacent?
No. Supplementary angles are defined purely by their sum being 180°. A linear pair (two adjacent angles sharing a vertex and a common ray that together form a straight line) is always supplementary, but supplementary angles need not form a linear pair — they can be located anywhere in a figure.
How are supplementary angles used in parallel line proofs?
When a transversal crosses two parallel lines, co-interior angles (same-side interior angles) are supplementary. This is one of the key theorems used to prove lines are parallel or to find unknown angles in geometric figures involving parallel lines and transversals.
Can an obtuse angle have a supplement?
Yes. Any angle strictly between 0° and 180° has a supplement. If the angle is obtuse (between 90° and 180°), its supplement is acute (between 0° and 90°), and vice versa. Only a right angle (90°) has a right-angle supplement.