How this calculator works
Two interior angles determine the third through the 180° angle sum. Side-based cases use the law of cosines, which distinguishes acute and obtuse angles without losing their supplementary relationship. In SAS mode choose the known included angle; only the two sides meeting there are requested. Each exterior angle is 180° minus the interior angle at the same vertex. The exterior equals the sum of the other two interior angles.
Formula
A+B+C=180°; cos C=(a²+b²-c²)/(2ab); exterior at A=180°-A=B+C.
Worked example
Angles A=35° and B=65° leave C=80°. For sides 3, 4 and 5, the angle opposite 5 is 90°, while the other two angles are approximately 36.869898° and 53.130102°.
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Frequently asked questions
Do I need a side to find the third angle?
No. Two angles determine all three angles. A side is needed only if you also want the triangle’s size.
Which angle is largest?
The angle opposite the longest side. The tool reports its value separately.
Are the exterior angles all below 180°?
For a non-flat triangle each interior angle is between 0° and 180°, so its supplementary exterior angle is also in that interval.