Supplementary Angles Calculator

Background.

Draw a straight line, put a point anywhere on it and send a second line off at any angle. The two angles on either side of that new line always add up to 180°, because together they make up the original straight line. Any two angles with that total are called supplementary, whether or not they sit side by side.

The idea turns up all over school geometry, usually as the one step that unlocks the rest of a diagram. Where a transversal crosses two parallel lines, the two interior angles on the same side are supplementary. Neighbouring angles in a parallelogram are supplementary, so knowing one angle gives all four. Opposite angles of a quadrilateral drawn inside a circle add to 180°. At each corner of a polygon, the interior angle and the exterior angle are supplementary, which is how a regular pentagon's 108° interior angle becomes a 72° exterior turn.

Supplementary angles also share a sine: sin 35° and sin 145° are both about 0.5736. That is the reason the sine rule can produce two different triangles from the same two sides and a non-included angle, the so-called ambiguous case.

Outside the classroom the most common use is checking a protractor reading. A protractor carries two scales running in opposite directions, and reading the wrong one gives the supplement of the angle you meant to measure. If an angle that is plainly acute reads as 145°, the true value is 35°.

What is supplementary angles calculator?

Two angles are supplementary when their measures add up to exactly 180 degrees, a straight angle; each is the supplement of the other. An acute angle always has an obtuse supplement, a right angle is its own supplement, and the supplement of an obtuse angle is acute. The angles do not have to be adjacent or even in the same figure; only the sum matters. In radians the total is π, so the supplement of θ is π − θ.

How to use this calculator.

1. 01Enter the angle you know in degrees, anywhere from 0° to 180°. Decimal degrees such as 37.5 are accepted.
2. 02If your angle is in radians, convert it first by multiplying by 180 and dividing by π.
3. 03Read the other angle, the one that makes the pair add to 180°.
4. 04For a parallelogram or a pair of co-interior angles, use the result directly; for a polygon, it converts an interior angle into the exterior angle at the same corner, or back again.

The formula.

Supplement = 180° − θ, where θ is the angle you know. The 180° is a straight angle, half a full turn of 360°, which is what two angles forming a straight line must cover between them. The relationship is symmetric: applying the subtraction twice returns the original angle. Because the result falls as the input rises, small angles have large supplements and vice versa, with 90° as the balance point where both angles are equal. Inputs are limited to 0° through 180°, since a supplement below zero would not be an angle in the usual geometric sense; at the extremes, 0° and 180° are each other's supplement. Compare complementary angles, which add to 90° instead.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.