1. What is the Triangle Angle Sum Theorem?

The Triangle Angle Sum Theorem states that the sum of the interior angles of any triangle is always 180 degrees. This fundamental principle is true for all types of triangles - scalene, isosceles, equilateral, acute, right, and obtuse.

2. How Does the Calculator Work?

The calculator uses the Triangle Angle Sum Theorem:

Where:

• \( \text{sum} \) — Total of all three interior angles
• Each angle is measured in degrees

Calculation: If two angles are known, the third angle is calculated by subtracting the sum of the known angles from 180°.

3. Importance of Angle Sum Calculation

Details: Understanding angle relationships in triangles is essential for solving geometric problems, proving theorems, and applications in trigonometry, architecture, and engineering.

4. Using the Calculator

Tips: Enter any two known angles (between 0° and 180°). The calculator will determine the third angle. All three angles must sum to exactly 180° in a valid triangle.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all types of triangles?
A: Yes, the angle sum theorem applies to all triangles regardless of their type or size.

Q2: What if my angles don't add up to 180°?
A: Then the figure is not a valid Euclidean triangle. Check your measurements or calculations.

Q3: Can I use this for right triangles?
A: Absolutely! In right triangles, the two non-right angles will always sum to 90°.

Q4: How precise should my angle measurements be?
A: For practical purposes, one decimal place is usually sufficient, but more precision may be needed for technical applications.

Q5: Does this apply to spherical triangles?
A: No, spherical triangles on a sphere's surface have angle sums greater than 180°.