Triangle Angles Calculator
Find missing angles (sum = 180°)
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Enter any two angles to find the third
Triangle Diagram
Triangle Angle Sum Theorem
The triangle angle sum theorem states that the sum of the three interior angles of any triangle always equals 180 degrees. This fundamental property applies to all triangles in Euclidean geometry.
Formula
A + B + C = 180°
Where A, B, and C are the three interior angles of the triangle.
Finding a Missing Angle
If you know two angles, you can find the third by rearranging the formula:
- C = 180° - A - B
- B = 180° - A - C
- A = 180° - B - C
Types of Triangles by Angles
- Acute Triangle: All three angles are less than 90°
- Right Triangle: One angle equals exactly 90°
- Obtuse Triangle: One angle is greater than 90°
Frequently Asked Questions
Why do triangle angles always add up to 180°?
This is a fundamental property of Euclidean geometry. It can be proven by drawing a line parallel to one side of the triangle through the opposite vertex, creating alternate interior angles.
Can a triangle have two right angles?
No, if a triangle had two 90° angles, their sum would already be 180°, leaving 0° for the third angle, which is impossible.
What if I only know one angle?
You need at least two angles to calculate the third using the angle sum theorem. With only one angle, infinite triangles are possible.
Does this work for all triangles?
Yes, the angle sum theorem applies to all triangles: acute, right, obtuse, scalene, isosceles, and equilateral triangles.
What's the largest possible angle in a triangle?
An angle must be less than 180°. In practice, for a valid triangle, if one angle approaches 180°, the other two approach 0°, making the triangle degenerate.
How do exterior angles relate to interior angles?
An exterior angle of a triangle equals the sum of the two non-adjacent interior angles. Also, an interior angle and its adjacent exterior angle sum to 180°.
What if my angles don't add up to 180°?
If three angles don't sum to 180°, they cannot form a valid triangle. Check your measurements for errors.
Does this rule work in radians?
Yes, in radians, the sum of angles in a triangle equals π (pi) radians, which is equivalent to 180 degrees.