Triangle Degree Calculator

Background.

The three angles inside any flat triangle add up to exactly 180°, so knowing two of them always gives away the third. That single fact does a surprising amount of work. It lets a roofer find the angle at the ridge from the angles at the eaves, lets a student close a geometry proof, and lets a surveyor check whether three measured angles agree with each other.

The reason is a short argument that goes back to Euclid. Draw a line through one corner of the triangle, parallel to the opposite side. The two angles this line makes with the triangle's other sides equal the triangle's two far angles, as alternate angles across parallel lines, and together with the angle at the corner they fill a straight line, which is 180°. The argument depends on the parallel postulate, which is why the rule holds on a flat page but not on a curved surface. On a sphere every triangle has more than 180°: one drawn from the North Pole down two meridians 90° apart to the equator has three right angles, 270° in all.

Two related results come almost free. An exterior angle, made by extending one side past a corner, equals the sum of the two interior angles at the other corners. And the size of the third angle settles the triangle's type: over 90° makes it obtuse, exactly 90° makes it right-angled.

Angles fix a triangle's shape but not its size. Every triangle with angles of 50°, 60° and 70° is a scaled copy of every other, so finding any side length takes at least one known side as well, and then the law of sines.

What is triangle degree calculator?

The third angle of a triangle is the interior angle left once the other two are known. It follows from the angle-sum theorem: in plane, or Euclidean, geometry the three interior angles of every triangle total 180°, which is π radians. Each angle has to be greater than 0°, so the two known angles must add up to less than 180°. The answer is in degrees, like the inputs, and it applies to triangles drawn on a flat surface rather than on a sphere or other curved surface.

How to use this calculator.

1. 01Enter the two angles you know in decimal degrees. Convert minutes first: 35° 30′ is 35.5°, because one minute is a sixtieth of a degree.
2. 02Make sure the two add up to less than 180°. A pair that reaches 180° leaves nothing for the third angle, and the page will refuse it.
3. 03For a right triangle, enter 90 as one angle and the known acute angle as the other.
4. 04Read the third angle. If you measured all three angles yourself, compare the answer with your own third reading; the gap between them is the combined error of your measurements.

The formula.

C = 180° − A − B, where A and B are the two known interior angles and C is the angle at the remaining corner. The 180° comes from the angle-sum theorem of Euclidean geometry rather than from measurement, so it is exact. Only the sum A + B matters: 50° and 60° give the same third angle as 30° and 80°, and every degree added to either known angle takes a degree off C. The page rejects any pair summing to 180° or more, since C would then be zero or negative. The same subtraction gives the exterior angle at the third corner, which is 180° − C, or simply A + B. Working in radians, the rule reads C = π − A − B.

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.