Triangle Degree Calculator

Enter two known angles of a triangle to find the missing third angle (A + B + C = 180°) and see whether it's acute, right, obtuse, equilateral, isosceles, or scalene.

Quick Facts

Angle sum theorem
A + B + C = 180°
The three interior angles of any triangle always add up to 180 degrees.
Right triangle
One angle = 90°
A triangle can have at most one right angle.
Acute vs. obtuse
All < 90° or one > 90°
Acute triangles have three angles under 90°; obtuse triangles have exactly one angle over 90°.

Your Results

Calculated
Angle C
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180° − A − B
All Three Angles
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A, B, and C listed together
Classification by Size
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Acute, right, or obtuse
Classification by Symmetry
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Equilateral, isosceles, or scalene (by angle)

Ready

Enter two known angles in degrees, then press Calculate.

Formula and Method for Finding a Triangle's Missing Angle

Every triangle's three interior angles always add up to exactly 180°, no matter its shape or size. This is the triangle angle sum theorem: A + B + C = 180°. If you know any two angles, you can find the third by subtraction: C = 180° − A − B. This calculator also classifies the triangle by the size of its largest angle (acute, right, or obtuse) and by how many of its angles are equal (equilateral, isosceles, or scalene).

How the calculation works

Enter two known interior angles, A and B, in degrees. The calculator subtracts their sum from 180° to find the third angle, C. It then checks the largest of the three angles: if it equals 90°, the triangle is a right triangle; if all three angles are under 90°, it is acute; if one angle exceeds 90°, it is obtuse. Separately, it compares all three angles to each other — three equal 60° angles make an equilateral triangle, two equal angles make an isosceles triangle, and three different angles make a scalene triangle.

Common mistakes

  • Entering angles that leave no room for a valid triangle: if A + B is 180° or more, there is no valid positive third angle — every triangle needs three positive angles that sum to exactly 180°.
  • Mixing up angle and side classification: "isosceles" and "equilateral" can describe matching angles or matching side lengths — the two always agree in a real triangle, but this calculator only looks at the angles you enter.
  • Assuming a triangle can have two right or obtuse angles: two angles of 90° or more would already sum to 180° or beyond, leaving no room for a positive third angle, so at most one angle can be 90° or greater.

Real-world applications

  • Carpentry and framing use the angle sum theorem to cut the third angle of a triangular brace or roof truss once two angles are set.
  • Surveying and navigation use triangle angle relationships to find an unknown bearing when two angles of a triangulated path are already known.
  • Geometry and trigonometry students use the angle sum theorem as the starting point for the Law of Sines and the Law of Cosines.
  • CAD and design software checks that drawn triangle angles sum to 180° to confirm the shape is geometrically valid.

Frequently Asked Questions

How do I find the third angle of a triangle?
Subtract the sum of the two known angles from 180°: C = 180° − A − B. For example, if A = 50° and B = 60°, then C = 180 − 50 − 60 = 70°.
What's the difference between acute, right, and obtuse triangles?
A triangle is acute if all three angles are less than 90°, right if exactly one angle equals 90°, and obtuse if exactly one angle is greater than 90°. A triangle can never have more than one angle that is 90° or greater.
Can a triangle have two right angles?
No. Two 90° angles would already sum to 180°, leaving 0° for the third angle, which is not a valid triangle. Every triangle has at most one angle that is 90° or greater.
What makes a triangle equilateral, isosceles, or scalene by its angles?
A triangle is equilateral if all three angles equal 60°, isosceles if exactly two angles are equal, and scalene if all three angles are different. Because angles and their opposite sides are directly related, angle-based and side-based classifications always match.

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