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
| Field | What to enter |
|---|---|
| Mode | Choose one: Find the supplement, Check two angles |
| Angle α | Units: °, rad, π rad, grad, turn |
| Angle β | Units: °, 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 (°) |
|---|---|
| 35 | 145 |
| 52.5 | 127.5 |
| 70 | 110 |
| 87.5 | 92.5 |
| 105 | 75 |
| 140 | 40 |
Formula
α + β = 180° (π rad) ⇒ β = 180° − α
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°.
Frequently asked questions
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.