Complementary and supplementary angles
Complement, supplement and explement
Result
Your answer appears here as you type.
Check two angles
About this tool
Find the complement, supplement and explement of an angle, or check whether two angles are complementary, supplementary or explementary.
What the terms mean
Two angles are complementary when they add up to 90°, like 30° and 60°. To find the complement of an angle, subtract it from 90°. Only angles smaller than 90° have one.
Two angles are supplementary when they add up to 180°, like 50° and 130°. To find the supplement, subtract the angle from 180°. Two angles that together form a straight line are always supplementary.
Two angles are explementary, or conjugate, when they add up to a full turn of 360°. The explement of 60° is 300°.
An easy way to remember: “complementary” comes before “supplementary” in the alphabet, just as 90° comes before 180°.
Where these angle pairs come up
- In every right triangle, the two acute angles are complementary, because together with the right angle they make 180°. Know one and you know the other.
- Along a straight line, two angles side by side are supplementary. That is how the angle on the far side of a beam, a ramp or a roof is found.
- Between parallel lines, the interior angles on the same side of a line crossing them are supplementary, the rule behind many geometry exercises. See angle pairs.
- Round a point, an angle and its explement fill a full turn, so the reflex angle on the other side of a 60° angle is 300°.
In radians the totals become π/2, π and 2π. To work with an angle in another unit, convert it first with the angle converter.
Frequently asked questions
How do you remember the difference between complementary and supplementary angles?
Think of the shapes they make: complementary angles fit together into a corner, 90°, and supplementary angles lie together along a straight line, 180°.
In English there is also a letter trick: C comes before S in the alphabet, just as 90 comes before 180.
How do you solve for x in complementary and supplementary angles?
Write an equation that sets the two angles equal to their total, 90° if they are complementary or 180° if they are supplementary, then solve it.
Example: two complementary angles measure x and 2x, so x + 2x = 90, 3x = 90 and x = 30: the angles are 30° and 60°. If two supplementary angles are (3x + 10)° and (2x − 5)°, then 5x + 5 = 180, so x = 35 and the angles are 115° and 65°. Check that pair with the checker above.
Can complementary or supplementary angles be adjacent or vertical?
Yes. Adjacent angles share a vertex and a side. Two adjacent angles that form a straight line, called a linear pair, are always supplementary, and two adjacent angles that fill a square corner are complementary.
Vertical angles, the ones opposite each other where two lines cross, are always equal. So they can only be complementary if each is 45°, and only supplementary if each is 90°. See angle pairs for a drawing you can move.
How do you find complementary and supplementary angles in radians?
Use π/2 in place of 90° and π in place of 180°. The complement of an angle x is π/2 − x, and its supplement is π − x.
For example, the complement of π/6 is π/2 − π/6 = π/3, and its supplement is π − π/6 = 5π/6. To work with decimals instead, convert the angle first with the angle converter.
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About these measurements
Readings are estimates taken from rendered pixels and consumer device sensors. Do not rely on them for structural engineering, surveying, manufacturing inspection, navigation, or medical decisions. Check anything safety-critical with a calibrated instrument.
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