1. What is the Triangle Angle Sum Theorem?

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. This fundamental geometric principle applies to all triangles, regardless of their type or size.

2. How Does the Calculator Work?

The calculator uses the Triangle Angle Sum Theorem:

Where:

• \( A \) — First angle in degrees
• \( B \) — Second angle in degrees
• \( C \) — Third angle in degrees

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, architecture, engineering, and various design fields. It helps in determining triangle types and solving complex geometric problems.

4. Using the Calculator

Tips: Enter any two angles of a triangle (must be positive numbers and their sum must be less than 180°). The calculator will determine the third angle.

5. Frequently Asked Questions (FAQ)

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

Q2: What if the sum of two angles equals or exceeds 180°?
A: This would violate the triangle angle sum theorem, indicating invalid input as no such triangle can exist.

Q3: Can this be used for right triangles?
A: Yes, in right triangles where one angle is 90°, the other two angles must sum to 90°.

Q4: How precise are the calculations?
A: Results are accurate to one decimal place, suitable for most practical applications.

Q5: Can this calculator determine if angles form a valid triangle?
A: Yes, if the sum of two angles is 180° or more, it indicates the angles cannot form a valid triangle.