1. What is the Triangle Sum Theorem?

The Triangle 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 or size.

2. How Does the Calculator Work?

The calculator uses the Triangle Sum Theorem equation:

Where:

• \( \angle1 \) — First known angle in degrees
• \( \angle2 \) — Second known angle in degrees
• \( \angle3 \) — Unknown angle to be calculated

Explanation: The theorem allows you to find the third angle when two angles are known by subtracting their sum from 180°.

3. Importance of the Theorem

Details: This theorem is essential in geometry for solving triangle problems, proving other theorems, and applications in trigonometry, architecture, and engineering.

4. Using the Calculator

Tips: Enter two known angles (must be positive numbers between 0-180°). Their sum must be less than 180° for a valid triangle.

5. Frequently Asked Questions (FAQ)

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

Q2: What if my two angles sum to 180° or more?
A: This would violate the theorem - such angles cannot form a valid triangle. The calculator will show no result in this case.

Q3: Can I use this for right triangles?
A: Absolutely! For right triangles, one angle is 90°, so the other two 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 be used for spherical geometry?
A: No, this theorem only applies to Euclidean (plane) geometry. Spherical triangles have angle sums greater than 180°.