Supplementary Angles Calculator

Created by Hanna Pamuła, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Mar 11, 2022

Welcome to the supplementary angle calculator. You don't need to rack your brain on how to find supplementary angles any more - read our supplementary angles definition or simply click through our tool, and everything should be clear! Also, this calculator will allow you to quickly check if two angles are supplementary.

Don't forget to check out the twin brother of this calculator - the complementary angles calculator.

What are supplementary angles? Supplementary angles definition

The adjective supplementary describes a special relationship between two angles. Specifically, according to a supplementary angles definition, these two angles sum up to 180° (or π if you're using radians).

non-adjacent supplementary angles

In other words, if they were adjacent, then they'd form a straight line.

adjacent supplementary angles

Also, keep in mind the important properties of supplementary angles:

  • Only two angles that sum up to 180° (π) are called supplementary angles. Three angles (or more) can - of course - sum up to that value, but they're not called supplementary angles. Like in a triangle - all three of the triangle's angles add up to 180°, but they aren't supplementary angles.
  • Your two supplementary angles cannot be both obtuse or both acute - there are only two options:
    • one angle is acute, and the other is obtuse.
    • both of them are right angles.

How to find supplementary angles?

Let's consider two probable scenarios - you're searching for a supplementary angle to your given angle, or you have two angles, and you're wondering if they are supplementary. Both questions may be solved with this supplementary angles calculator:

  • 1st scenario: What is the supplementary angle?

    Subtract your given angle from 180°:

    supplementary angle = 180° - angle

    or in π rad:

    supplementary angle = π - angle

  • 2nd scenario: Are these two angles supplementary?

    Check if their sum equals 180°:

    angle1 + angle2 = 180° (π) - the angles are complementary

    angle1 + angle2 ≠ 180° (π) - the angles are not complementary

So, for example, are these two angles supplementary?

  • 30° and 150° are supplementary (as they add up to 180°)
  • 2π/3 and π/3 are supplementary (as they sum up to π)
  • but 60° and 140° are not supplementary

Check your calculations with our supplementary angles calculator!

Adjacent supplementary angles

Searching for the adjacent supplementary angles in geometry is so frequent and natural that you may not even realize you're doing so! You're using the supplementary angles definition every time you have two lines or line segments that intersect (linear pair), as they form pairs of adjacent angles that are supplementary:

adjacent supplementary angles examples

And where can you find non-adjacent supplementary angles?

  • For example, in a parallelogram - the consecutive angles are supplementary in any parallelogram.
  • Also, as a parallelogram is a special case of a rhombus, a rectangle or even a square, the consecutive angles in these shapes are also non-adjacent supplementary angles.
  • In a trapezoid, leg angles are supplementary (as the leg intersects a pair of parallel lines that contain the trapezoid's bases)
non-adjacent supplementary angles examples

Can you think of some other examples?

Supplementary angles relationships

Knowing that two angles are supplementary is useful when you deal with trigonometric functions. Particularly, if you know that α and β are supplementary angles (α + β = 180° (π)), then you automatically will know that:

  • the sines of the supplementary angles are equal

    sin(α) = sin(β)

  • the cosine of an angle is the negative of its supplement

    cos(α) = -cos(β)

  • similarly the tangents of the supplementary angles are equal with opposed signs (unless tangent is undefined)

    tan(α) = -tan(β)

Hanna Pamuła, PhD candidate
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non-adjacent supplementary angles
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