Supplementary Angles Calculator

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).

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

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

• Only two angles that sum up to 180° (π) are supplementary. Three (or more) can - of course - sum up to that value (that happens in the triangle angle calculator), but they're not 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.

Let's consider two probable scenarios - you're searching for a supplementary angle to your given angle, or you have two angles, and you wonder if they are supplementary. You can solve both questions 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!

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 definition of the supplementary angle every time you have two lines or line segments that intersect (linear pair), as they form pairs of adjacent angles that are supplementary:

And where can you find non-adjacent supplementary angles?

• For example, in a parallelogram - the consecutive angles are supplementary in any parallelogram.
• 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).

Can you think of some other examples?

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 figure out 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 the tangent is undefined)

  tan(α) = -tan(β)

You can learn more about those functions in our trigonometric functions calculator.