Triangle Sum Theorem Calculator
Find a missing interior angle or verify if three angles form a valid triangle using the triangle sum theorem (sum = 180 deg). Free online geometry tool for students.
About This Calculator
The Triangle Sum Theorem is a fundamental rule in geometry that states the sum of all three interior angles in any triangle equals 180 deg (or pi radians). This property holds true for every triangle -- whether it is acute, right, obtuse, equilateral, isosceles, or scalene.
Mathematically, the theorem is expressed as: alpha + beta + gamma = 180 deg, where alpha, beta, and gamma are the three interior angles. If you know any two angles, you can always find the third using: gamma = 180 deg - alpha - beta.
This calculator serves two purposes. Enter any two angles and it will compute the missing third angle for you. Or enter all three angles to verify whether they form a valid triangle by checking if their sum equals 180 deg. This is especially useful for students checking their homework, teachers preparing geometry problems, or anyone working with triangle measurements.
The theorem can be proven by drawing a line parallel to one side through the opposite vertex. When a transversal cuts parallel lines, alternate interior angles are equal, proving that the three angles of the triangle always add up to a straight line (180 deg).
Frequently Asked Questions
What is the triangle sum theorem?
The triangle sum theorem states that the sum of all three interior angles in any triangle equals 180 deg. This is true for all triangles regardless of their shape or size.
How do I find a missing angle using this calculator?
Enter any two known angles in degrees and leave the third field blank. The calculator will automatically compute the missing angle using the formula: Missing Angle = 180 deg - Angle1 - Angle2.
What happens if the three angles do not sum to 180 deg?
If the three angles do not add up to 180 deg within a tolerance of 0.01 deg, the calculator marks the triangle as invalid. This can happen when the entered angles do not correspond to a real triangle.
Can a triangle have two right angles?
No, a triangle cannot have two right angles (90 deg each). Two right angles would sum to 180 deg, leaving 0 deg for the third angle, which would form a degenerate line rather than a triangle. The maximum any triangle can have is one right angle or one obtuse angle.
What is the difference between interior and exterior angles?
Interior angles are the angles inside the triangle at each vertex. The exterior angle is formed by extending one side of the triangle outward. The exterior angle equals the sum of the two opposite interior angles, and it is supplementary to its adjacent interior angle.
Can I enter angles in radians instead of degrees?
This calculator currently accepts angles in degrees only. To convert radians to degrees, multiply the radian value by 180/pi. For example, pi/3 radians equals 60 deg.
Is the triangle sum theorem the same for all types of triangles?
Yes, the triangle sum theorem applies to all triangles -- acute, right, obtuse, equilateral, isosceles, and scalene. Every triangle has interior angles that sum to exactly 180 deg.