Triangle Angles Calculator — Interior & Exterior Angles
Enter any two interior angles of a triangle and this calculator finds the third using the angle-sum property (A + B + C = 180°). It also computes all three exterior angles, verifies the exterior-angle sum (360°), and classifies the triangle by angle type and side symmetry.
°
°
C = 180° − A − B (interior angles of a triangle always sum to 180°)
- 1
Sum of known angles
60 + 60 = 120 - 2
Third interior angle C
180 − 120 = 60Interior angles of any triangle always sum to 180°.
How does this calculator work?
In any flat (Euclidean) triangle, interior angles A + B + C = 180°, so the third angle is C = 180° − A − B. Each exterior angle = 180° minus its interior angle; the three exterior angles always sum to 360°. Enter two angles to find the third — the triangle is also classified as acute/right/obtuse and scalene/isosceles/equilateral.
Formula
How this is calculated
The interior angle-sum theorem states that the three interior angles of any triangle in Euclidean geometry always add up to exactly 180°. This lets us find the third angle as C = 180° − A − B whenever we know the other two — a fundamental result provable from the parallel postulate.
Each exterior angle is formed by extending one side of the triangle beyond a vertex. The exterior angle at any vertex equals 180° minus the interior angle at that vertex (since the interior and exterior angles are supplementary). Summing all three exterior angles gives 360° — always, for any triangle. A related result is the Exterior Angle Theorem: the exterior angle at one vertex equals the sum of the two non-adjacent (remote) interior angles: e.g. exterior at C = A + B.
Triangles are classified two ways. By angles: all angles less than 90° = acute; one angle exactly 90° = right; one angle greater than 90° = obtuse. By side symmetry (derived from angle equality — equal angles imply equal opposite sides): all three angles equal (60° each) = equilateral; exactly two angles equal = isosceles; all angles different = scalene.
Frequently asked questions
This calculator uses degrees only. To convert radians to degrees multiply by 180/π (approximately 57.2958). For example, π/3 radians = 60°. Enter the result in degrees.
The exterior angle at any vertex of a triangle equals the sum of the two remote interior angles (the interior angles at the other two vertices). For example, exterior angle at C = A + B. This follows directly from the fact that interior angles sum to 180° and the interior and exterior angles at a vertex are supplementary.
No — the 180° sum is a consequence of Euclidean (flat) geometry. On the surface of a sphere (spherical geometry), the sum of a triangle's angles exceeds 180° (up to 540° for a triangle covering a full hemisphere). In hyperbolic geometry, the sum is less than 180°. This calculator applies only to flat (Euclidean) triangles.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Angles Calculator — Interior & Exterior Angles [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/interior-and-exterior-triangle-angles-calculator
TG we-Calculate Editorial Team. "Triangle Angles Calculator — Interior & Exterior Angles." TG we-Calculate. 2026. https://we-calculate.com/calculator/interior-and-exterior-triangle-angles-calculator.
TG we-Calculate Editorial Team, "Triangle Angles Calculator — Interior & Exterior Angles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/interior-and-exterior-triangle-angles-calculator
@misc{wecalculate_interior_and_exterior_triangle_angles_calculator, title = {Triangle Angles Calculator — Interior & Exterior Angles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/interior-and-exterior-triangle-angles-calculator}}, year = {2026}, note = {TG we-Calculate} }
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