1. Triangle Angle Sum Theorem

The fundamental rule of triangles states that the sum of interior angles in any triangle always equals 180 degrees. This principle holds true for all types of triangles - scalene, isosceles, equilateral, acute, right, and obtuse.

2. How the Calculator Works

The calculator uses the Triangle Angle Sum Theorem:

Where:

• \( \theta_1 \) — First angle of the triangle
• \( \theta_2 \) — Second angle of the triangle
• \( \theta_3 \) — Third angle of the triangle

Explanation: When you know two angles of a triangle, the third can be found by subtracting the sum of the known angles from 180°.

3. Importance of Angle Calculation

Details: Calculating missing angles is essential in geometry, trigonometry, architecture, engineering, and various design fields. It helps in determining the shape and properties of triangles.

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: Can this calculator work with right triangles?
A: Yes, simply enter 90° as one of the angles and one other angle to find the third.

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

Q3: Can angles be negative or zero?
A: No, triangle angles must be greater than 0° and less than 180°.

Q4: Does this work for all types of triangles?
A: Yes, the angle sum theorem applies to all triangles regardless of their type or size.

Q5: What if the sum of two angles equals or exceeds 180°?
A: This would violate the triangle angle sum theorem, indicating invalid input (not a valid triangle).