Exterior Angles of a Triangle Calculator
Enter any two interior angles of a triangle to instantly find the third interior angle and all three exterior angles. The calculator also verifies the exterior angle theorem: each exterior angle equals the sum of the two non-adjacent (remote) interior angles.
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Third interior angle: C = 180° − A − B
- 1
Triangle angle-sum theorem
A + B + C = 180°The three interior angles of any triangle always sum to 180°. - 2
Solve for C = 180° − A − B
180° − 60 − 70 = 50
How does this calculator work?
Enter two interior angles (A and B); C = 180° − A − B. Each exterior angle = 180° minus its interior angle, and each also equals the sum of the two remote interior angles (the Exterior Angle Theorem). All three exterior angles sum to exactly 360° for any valid triangle.
Formula
How this is calculated
A triangle's three interior angles always add to 180°, so entering any two (A and B) immediately gives the third: C = 180° − A − B. An exterior angle at a vertex is formed by extending one side of the triangle beyond that vertex; it is the supplement of the interior angle at the same vertex, so exterior angle = 180° − interior angle.
The exterior angle theorem states that each exterior angle equals the sum of the two non-adjacent interior angles (called the remote interior angles). For example, the exterior angle at vertex A equals B + C. This is a direct consequence of the triangle angle sum: if A + B + C = 180° and the exterior angle at A is 180° − A, then exterior_A = B + C. The theorem is useful in proofs and is testable in geometry courses.
For any convex polygon, the sum of one exterior angle at each vertex is always 360°. For a triangle this means exterior_A + exterior_B + exterior_C = 360°, which this calculator confirms. All angles must be strictly positive and the sum of any two must be less than 180° for a valid (non-degenerate) triangle.
Frequently asked questions
The exterior angle theorem states that the exterior angle of a triangle (the angle formed by one side and the extension of an adjacent side) is equal to the sum of the two non-adjacent interior angles. So if the interior angles are A, B, C, the exterior angle at vertex A is B + C = 180° − A.
Each exterior angle is the supplement of its interior angle: ext_A + A = 180°, so ext_A = 180° − A. Summing all three: ext_A + ext_B + ext_C = 540° − (A + B + C) = 540° − 180° = 360°. This holds for any convex polygon — one exterior angle per vertex always sums to 360°.
Yes. An obtuse triangle has one interior angle greater than 90°. Its exterior angle at the obtuse vertex will be less than 90°. The calculator handles all valid triangles as long as both entered angles are positive and their sum is less than 180°.
Also known as
TG we-Calculate Editorial Team. (2026). Exterior Angles of a Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/exterior-angles-of-a-triangle-calculator
TG we-Calculate Editorial Team. "Exterior Angles of a Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/exterior-angles-of-a-triangle-calculator.
TG we-Calculate Editorial Team, "Exterior Angles of a Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/exterior-angles-of-a-triangle-calculator
@misc{wecalculate_exterior_angles_of_a_triangle_calculator, title = {Exterior Angles of a Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/exterior-angles-of-a-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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