How this calculator works
An exterior angle here is made by extending one side at a vertex and taking the angle adjacent to the triangle’s interior. It is supplementary to that interior, so first convert any exterior inputs by subtracting them from 180°. The two resulting interiors determine the third. The table compares each exterior with the sum of the two interiors at the other vertices. Choosing one such exterior at each vertex gives a full turn, or 360°.
Formula
A+B+C=180°; E_A=180°-A=B+C, and likewise at B and C. E_A+E_B+E_C=360°. For two exterior inputs E_A,E_B, C=E_A+E_B-180°.
Worked example
Exterior angles 140° at A and 110° at B give interiors A=40° and B=70°. The third interior is 70°, so its exterior is 110°. The three exteriors total 140°+110°+110°=360°.
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Frequently asked questions
Can I mix an interior and an exterior input?
Yes. Choose each input type independently and make sure the known angles belong to the two selected vertices.
Why must two exterior inputs add to more than 180°?
Their sum minus 180° is the third interior angle. That angle must be positive for a non-flat triangle.
Do you mean the reflex angle outside the triangle?
No. This tool uses the supplementary exterior between 0° and 180°, formed by extending one side. A reflex outside angle would be 360° minus the interior.