# Supplementary Angles Calculator

URL: https://speedycalculator.com/calculators/math/supplementary-angles/
Last updated: 2026-10-30

> The supplementary angles calculator finds the supplement of an angle (180° minus the angle) in degrees or radians, or checks whether two angles are supplementary.

## Inputs

- Mode
- Angle α (°, rad, π rad, grad, turn)
- Angle β (°, rad, π rad, grad, turn)

## Results

- Supplement 180° − α
- In radians
- Are they supplementary?
- Sum α + β

## Formula

```
α + β = 180° (π rad)  ⇒  β = 180° − α
```

## Explanation

Two angles are supplementary when they add up to a straight angle. Angles on a straight line, co-interior angles between parallel lines and opposite angles of a cyclic quadrilateral are supplementary.

### How to use the Supplementary Angles Calculator

- **Mode**
- **Angle α**
- **Angle β**

Results update as you type, and everything is calculated in your browser.

### How it works

Choose to find a supplement or to check a pair. Angles between 0° and 180° have a positive supplement.

### Tips

- Angles are measured counter-clockwise from the positive x-axis by default.
- Add or subtract 360° (2π) to move between coterminal angles.
- Complementary angles add to 90°, supplementary angles to 180°.
- Use the unit menu to switch between degrees, radians and gradians.

### Common mistakes to avoid

- Mixing up complementary and supplementary angles.
- Forgetting that a reference angle is always between 0° and 90°.
- Leaving an angle in radians when the question asks for degrees.

### Inputs explained

FieldWhat to enterModeChoose one: Find the supplement, Check two anglesAngle αUnits: °, rad, π rad, grad, turnAngle βUnits: °, rad, π rad, grad, turn

### What each result means

- **Supplement 180° − α** = 180 - [Angle α]
- **In radians** = rad(180 - [Angle α])
- **Sum α + β** = [Angle α] + [Angle β]

### Example values

How the main result changes when **Angle α** changes and everything else stays at the example values above:

Angle α (°)Supplement 180° − α (°)3514552.5127.57011087.592.51057514040

## Worked example

Inputs — Mode: Find the supplement; Angle α: 70 °.

Results — **Supplement 180° − α = 110 °**; In radians = 1.91986218 rad.

## Key terms

- **Supplementary angles**: Two angles summing to 180°.

## FAQ

**What is the supplement of 120°?**
60°.

**Are angles on a straight line supplementary?**
Yes – they add to 180°.

**Do supplementary angles have the same sine?**
Yes: sin(180° − α) = sin α.

**What is a linear pair?**
Two adjacent supplementary angles.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [Wolfram MathWorld – Supplementary angles](https://mathworld.wolfram.com/SupplementaryAngles.html)