Triangle Sum Theorem Calculator — Find the Missing Angle
The interior angles of every triangle always add up to exactly 180°. Enter any two angles — the calculator finds the third and classifies the triangle as acute, right or obtuse.
°
°
°
180° − (sum of the other two angles)
- 1
Sum of known angles A + B
55° + 75° = 130° - 2
Missing angle C = 180° − (A + B)
180° − 130° = 50°Interior angles of every triangle sum to exactly 180°.
How does this calculator work?
Every triangle's interior angles sum to 180° (the triangle angle-sum theorem). To find the missing angle, subtract the other two from 180°: C = 180° − A − B. Enter any two angles and the calculator returns the third, classifies the triangle as acute / right / obtuse, and confirms the 180° sum.
Formula
How this is calculated
The triangle angle-sum theorem (also called the interior angle theorem) is one of the most fundamental results in Euclidean geometry: the three interior angles of any triangle always sum to exactly 180°. This holds for all triangles — scalene, isosceles, equilateral, right, acute or obtuse — in flat (Euclidean) space.
To find a missing angle, subtract the sum of the two known angles from 180°: C = 180° − A − B. The only constraint is that the two known angles must each be positive and their sum must be strictly less than 180°; otherwise no valid triangle exists.
Once all three angles are known the calculator classifies the triangle: if every angle is less than 90° it is acute; if one angle equals exactly 90° it is right; if one angle exceeds 90° it is obtuse. In any triangle at most one angle can be ≥ 90°, since two such angles would already sum to at least 180°.
Frequently asked questions
One proof: draw a line parallel to side BC through vertex A. By alternate interior angles, the angles on either side of A (along the parallel line) equal B and C respectively. Together with angle A they fill a straight line (180°). This proof relies on Euclid's parallel postulate and holds in flat Euclidean geometry.
No — two right angles alone sum to 180°, leaving 0° for the third angle, which is impossible. Similarly, a triangle cannot have two obtuse angles. Every triangle has at most one right angle and at most one obtuse angle.
No — on a sphere (spherical geometry) the interior angles of a triangle sum to more than 180°. For example, a triangle formed by the equator and two meridians 90° apart has three right angles (270° total). The sum theorem holds only in flat (Euclidean) geometry.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Sum Theorem Calculator — Find the Missing Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-sum-theorem-calculator
TG we-Calculate Editorial Team. "Triangle Sum Theorem Calculator — Find the Missing Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-sum-theorem-calculator.
TG we-Calculate Editorial Team, "Triangle Sum Theorem Calculator — Find the Missing Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-sum-theorem-calculator
@misc{wecalculate_triangle_sum_theorem_calculator, title = {Triangle Sum Theorem Calculator — Find the Missing Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-sum-theorem-calculator}}, year = {2026}, note = {TG we-Calculate} }
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