Math calculator
Both at once — and the cases where neither one exists.
90° for a complement, 180° for a supplement.
35° is acute
complement 55°
Complement 55°, supplement 145° — the two add with your angle to 90° and 180°.
Complement (to 90°)
55°
35° + 55° = 90°
Supplement (to 180°)
145°
35° + 145° = 180°
Explement (to 360°)
325°
what is left of a full turn
Classification
acute
by size
Where it sits
The two marks are 90° and 180°. Left of the first, an angle has both a complement and a supplement. Between them, only a supplement. Past the second, neither.
A missing complement is reported as missing rather than as a negative number, which is what it would be.
35° has a complement of 55° and a supplement of 145°. 120° has a supplement of 60° and no complement at all, because nothing positive can be added to it to reach 90°. That second case is the one most tools get wrong.
Exact degrees; missing answers reported as missing.
Updated 7 September 2026 · Works in any browser, no installation
Complementary angles add to 90°; supplementary angles add to 180°. So the complement of 35° is 55° and its supplement is 145°. The catch is that both have to be positive: an angle of 120° has a supplement of 60° but no complement, because there is no positive angle you can add to 120° to reach 90°.
At a glance
The names are easy to swap, and there is a reliable way not to.
C comes before S in the alphabet, and 90 comes before 180. Complementary is the smaller pair; supplementary is the larger one.
Another version some people prefer: complementary angles form a corner, a right angle; supplementary angles form a straight line. Both start with the same letter as the word they go with.
Ask for the complement of 120° and the subtraction gives −30°. That is not an answer; it is a sign that the question has none.
Angles in this sense are positive quantities. There is no positive angle you can add to 120° to reach 90°, because 120° has already gone past it. So only acute angles — strictly between 0° and 90° — have complements at all.
Supplements are the same one threshold up. Only angles below 180° have one, so a reflex angle of 200° has neither.
Some tools return the negative number anyway. That is worse than useless: it looks like an answer and it is not one. This page says which of the two exist and why the other does not.
The edge cases are worth stating too. 90° has no complement, because the only candidate is 0° and a zero angle is degenerate. 180° has no supplement, for the same reason.
Two angles that add to 360° are explementary, also called conjugate angles. The word turns up far less often than the other two, and the idea turns up constantly.
Any angle drawn at a point has two: the one you meant and the reflex one going the other way round. They add to a full turn. The clock-angle question is exactly this — 75° one way and 285° the other.
Unlike the other two, this one always exists. Every angle has an explement, including reflex ones, because 360° minus anything below 360° is positive.
Right triangles. The two non-right angles always add to 90°, so they are complementary. Knowing one gives the other immediately.
Angles on a straight line. They add to 180°, so two of them are supplementary. This is the fact behind most “find the missing angle” problems.
Parallel lines. Co-interior angles are supplementary; alternate and corresponding angles are equal. Distinguishing which is which is most of the work in those problems.
Cyclic quadrilaterals. Opposite angles are supplementary. It is a genuinely surprising result and it is used constantly in circle geometry.
Parallelograms. Adjacent angles are supplementary, which is why knowing one angle gives all four.
The word cosine is short for complementary sine, and the relationship is exactly that.
sin(θ) = cos(90° − θ). The sine of an angle equals the cosine of its complement. So sin 30° = cos 60°, both 0.5. The same holds for tangent and cotangent, and for secant and cosecant — every “co-” function is the original one applied to the complement.
Supplements have their own identity: sin(θ) = sin(180° − θ). Supplementary angles share a sine, which is precisely why the sine rule can give two possible triangles from the same data.
A point that trips people up: complementary and supplementary angles do not have to touch.
35° and 55° are complementary whether they sit side by side forming a right angle or appear in two different diagrams on two different pages. The definition is about the sum, not the position.
When they ARE adjacent, the terms are sometimes used: two adjacent supplementary angles form a linear pair, and two adjacent complementary angles form a right angle. Those are extra facts about a configuration, not part of the definitions.
The definitions and their positivity condition are standard; these are the references.
Method. Degrees are carried as exact rationals, so 22.5° gives 67.5° rather than 67.49999999999999. Existence is tested rather than assumed: a complement is returned only when the angle is strictly between 0° and 90°, and the page reports the absence with the reason rather than printing the negative number the subtraction would give. The suite checks that complement, supplement and explement each add back to their threshold for every acute whole degree. That engine is verified on every change against 82 hand-written assertions, including that complement, supplement and explement add back to 90°, 180° and 360° for all 89 acute whole degrees, and that 90°, 120° and 180° are each refused the answers they do not have. The count and the per-case breakdown are published on the formula verification page.
The acute angle a ray makes with the x-axis is a different quantity — that is the reference angle, and the Reference Angle Calculator computes it along with the sign of each trig function.
Educational use disclaimer
This is an educational tool. Degrees are carried as exact fractions; the convention that complements and supplements must be positive is the standard one, and the page states when it makes an answer impossible.
How we calculate · Found an error? email us
Published 7 September 2026