Complementary Angle Calculator
This complementary angle calculator gives the complement and the supplement of an angle. For 40° the complement is 50° and the supplement is 140°. It also solves the classic word problem: two supplementary or complementary angles whose difference you know.
Example: What do you want to find: Complement and supplement of an angle · Angle α 40 ° · Minutes 0 ′ · Seconds 0 ″ → Result: Complement 50° · supplement 140°. Source: OpenStax Prealgebra 2e, 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem – supplementary angles add to 180°, complementary angles add to 90°; Example 9.16 (40° → supplement 140°, complement 50°), Example 9.17 (supplementary, larger 30° more → 75° and 105°), Try It 9.31–9.34 (read 10.10.2026). Updated: .
How it is calculated
Two angles are complementary if they add up to 90° and supplementary if they add up to 180°. So the complement of α is 90° − α and the supplement is 180° − α. This is how the textbook OpenStax Prealgebra defines them; its example: an angle of 40° has the supplement 180° − 40° = 140° and the complement 90° − 40° = 50°. A tip from the book: “complementary” and “supplementary” are in alphabetical order, just like 90 and 180 are in numerical order.
Complement and supplement of common angles
| Angle α | Complement | Supplement |
|---|---|---|
| 40° | 50° | 140° |
| 25° | 65° | 155° |
| 77° | 13° | 103° |
| 30° | 60° | 150° |
| 45° | 45° | 135° |
| 60° | 30° | 120° |
| 89° | 1° | 91° |
| 27.5° | 62.5° | 152.5° |
| 120° | — | 60° |
| 150° | — | 30° |
Angles of 90° or more have no complement, because two positive angles cannot then add up to 90°. In the same way, only angles below 180° have a supplement. For larger angles the calculator shows what is missing to a full turn: 360° − α (calculated).
Two angles from sum and difference
A typical exercise: “Two angles are supplementary. The larger angle is 30° more than the smaller angle.” If the smaller angle is x, then x + (x + 30°) = 180°, so x = 75° and the larger angle is 105°. In general: smaller = (sum − difference) ÷ 2, larger = (sum + difference) ÷ 2.
| Sum | Difference | Smaller angle | Larger angle |
|---|---|---|---|
| 180° | 30° | 75° | 105° |
| 180° | 100° | 40° | 140° |
| 90° | 40° | 25° | 65° |
| 90° | 10° | 40° | 50° |
Sine, cosine and tangent of an angle are found with the sin cos tan calculator; the angles inside a triangle, which add up to 180°, are solved by the triangle calculator.
Frequently asked questions
How do you find the complement of an angle?
Subtract it from 90°. The complement of 40° is 90° − 40° = 50°. Only angles smaller than 90° have a complement.
How do you find the supplement of an angle?
Subtract it from 180°. The supplement of 40° is 180° − 40° = 140°; the supplement of 120° is 60°.
Can an angle of 120° have a complement?
No. 120° is already more than 90°, so no positive angle added to it gives 90°. It does have a supplement: 60°.
How do I enter degrees, minutes and seconds?
Enter the whole degrees, then minutes and seconds in their own fields. 27° 30′ is 27.5°; its complement is 62.5° = 62° 30′.
Two angles are complementary and differ by 40°. What are they?
(90° − 40°) ÷ 2 = 25° and (90° + 40°) ÷ 2 = 65°. Check: 25° + 65° = 90°.
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