Supplementary Angles Calculator
Enter any angle between 0° and 180° to instantly find its supplementary angle — the angle that, paired with yours, makes a straight line of 180°. The calculator also shows the complementary angle (when valid) and the trig identities linking the pair.
°
The angle that, together with yours, sums to 180°
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Input angle θ
θ = 65° = 65° - 2
Supplement = 180° − θ
180° − 65° = 115°
How does this calculator work?
The supplement of angle θ is 180° − θ. Two supplementary angles together form a straight line. The key trig identities are: sin(180°−θ) = sin θ, cos(180°−θ) = −cos θ, and tan(180°−θ) = −tan θ. Enter any angle from 0° to 180° to get its supplement instantly.
Formula
How this is calculated
Two angles are supplementary when they add up to exactly 180° — the angle formed by a straight line. So the supplement of any angle θ is simply 180° − θ. This appears constantly in geometry: interior angles of a quadrilateral, co-interior (same-side interior) angles formed by a transversal crossing parallel lines, and any time you need the angle on the other side of a straight edge.
The trig identities follow from the unit-circle definition of sine and cosine. Reflecting a point at angle θ across the y-axis gives the point at 180°−θ. The y-coordinate (sine) is unchanged, so sin(180°−θ) = sin θ. The x-coordinate (cosine) flips sign, so cos(180°−θ) = −cos θ. Dividing gives tan(180°−θ) = −tan θ. These are essential for solving equations in the second quadrant and appear throughout Fourier analysis and wave physics.
If the entered angle is less than 90°, the calculator also shows the complementary angle (90° − θ) for reference, since complementary and supplementary angles are often studied together.
Frequently asked questions
Supplementary angles are any two angles that sum to 180°. They form a straight line when placed adjacent to each other. The supplement of 65° is 115°, for example, since 65 + 115 = 180.
Yes — a 90° angle is its own supplement, since 180° − 90° = 90°. A right angle is the only angle that equals its supplement.
On the unit circle, the point at angle 180°−θ is the mirror image of the point at angle θ reflected across the y-axis. The y-coordinate (sine) stays the same; the x-coordinate (cosine) becomes negative. So sin is preserved but cos flips.
Also known as
TG we-Calculate Editorial Team. (2026). Supplementary Angles Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/supplementary-angles-calculator
TG we-Calculate Editorial Team. "Supplementary Angles Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/supplementary-angles-calculator.
TG we-Calculate Editorial Team, "Supplementary Angles Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/supplementary-angles-calculator
@misc{wecalculate_supplementary_angles_calculator, title = {Supplementary Angles Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/supplementary-angles-calculator}}, year = {2026}, note = {TG we-Calculate} }
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