How complementary and supplementary angles work
Use the calculator
Enter one angle from 0° through 180° and select Calculate. The supplement is 180° minus the angle. The complement is 90° minus the angle only when the input is no greater than 90°.
If the input is over 90°, the calculator says that no nonnegative complement exists instead of showing a negative angle. Editing the input immediately clears the old result.
Definitions
Two angle measures are complementary when their sum is 90°, a right angle. They are supplementary when their sum is 180°, a straight angle. The measures need not be adjacent unless the geometry problem also says they form a pair at one vertex.
The formulas are complement = 90° − θ and supplement = 180° − θ. This page intentionally uses degrees and the stated 0°–180° input range.
Boundaries and interpretation
At θ = 90°, the complement is 0° and the supplement is 90°. At θ = 180°, the supplement is 0° and there is no nonnegative complement.
A zero result is a boundary measure, not a drawn interior angle. Check whether your textbook or application requires strictly positive angles.
Worked examples
Acute angle
For 35°, the complement is 55° because 35° + 55° = 90°. The supplement is 145° because 35° + 145° = 180°.
Obtuse angle
For 120°, the supplement is 60°. A nonnegative complement does not exist because 90° − 120° would be −30°.
Frequently asked questions
Are supplementary angles always next to each other?
No. Their measures only need to total 180°; adjacency is an extra geometric condition.
Can an obtuse angle have a complement?
Not as a pair of nonnegative angles summing to 90°.
What is the complement of 90°?
The boundary value is 0°. Some contexts reserve “angle” for positive measures, so follow the problem’s convention.
Does this calculator accept radians?
No. This focused page accepts degrees from 0 through 180.