1. What is the Triangle Angle Sum Theorem?

The Triangle Angle Sum Theorem states that the sum of the interior angles of any triangle equals 180 degrees. This fundamental geometric principle applies to all triangles, regardless of their type (acute, obtuse, right, scalene, isosceles, or equilateral).

2. How Does the Calculator Work?

The calculator uses the Triangle Angle Sum Theorem:

Functionality:

• Enter any two known angles to calculate the third missing angle
• Enter all three angles to verify they sum to 180°
• Calculations are performed in degrees

3. Importance of Angle Calculation

Details: Knowing how to calculate missing angles in triangles is essential for solving geometry problems, architectural design, engineering calculations, and computer graphics applications.

4. Using the Calculator

Tips:

• Leave one field blank to calculate the missing angle
• Fill all three fields to verify the angles form a valid triangle
• Angles must be between 0° and 180°
• The sum of any two angles must be less than 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 - acute, obtuse, right, equilateral, isosceles, and scalene.

Q2: What if my angles don't sum to 180°?
A: If three entered angles don't sum to 180°, they cannot form a valid Euclidean triangle. Check your measurements.

Q3: Can I use this for spherical triangles?
A: No, this calculator is for plane (Euclidean) geometry only. Spherical triangles have angle sums greater than 180°.

Q4: How precise are the calculations?
A: Calculations are precise to one decimal place. Results are rounded for display.

Q5: What if two angles sum to 180° or more?
A: This would violate the triangle inequality theorem. No valid triangle can have two angles that sum to ≥180°.