1. What is the Triangle Angle Sum Theorem?

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle always equals 180 degrees. This fundamental geometric principle allows us to calculate unknown angles when two angles are known.

2. How Does the Calculator Work?

The calculator uses the Triangle Angle Sum Theorem:

Where:

• \( A \) — First angle of the triangle
• \( B \) — Second angle of the triangle
• \( C \) — Third angle of the triangle

Explanation: When two angles are known, the third can be calculated by subtracting their sum from 180°.

3. Importance of Angle Calculation

Details: Calculating unknown angles is essential in geometry, trigonometry, and various practical applications like construction, navigation, and engineering.

4. Using the Calculator

Tips: Enter any two known angles (in degrees) and leave the third field empty. The calculator will compute the missing angle. All angles must be between 0° and 180°.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all types of triangles?
A: Yes, the angle sum theorem applies to all triangles - equilateral, isosceles, scalene, right, acute, and obtuse.

Q2: What if I know only one angle?
A: You need at least two angles to calculate the third. With only one angle, there are infinite possible combinations for the other two.

Q3: Can angles be negative or zero?
A: In a valid triangle, all angles must be greater than 0° and less than 180°.

Q4: What if the sum of two angles is 180° or more?
A: This would violate the triangle inequality theorem, meaning such angles cannot form a valid triangle.

Q5: How precise are the calculations?
A: Results are calculated to one decimal place for precision in most practical applications.