1. What is the Triangle Sum Theorem?

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

2. How Does the Calculator Work?

The calculator uses the Triangle Sum Theorem:

Where:

• angle1 — First interior angle (degrees)
• angle2 — Second interior angle (degrees)
• angle3 — Third interior angle (degrees)

Explanation: The calculator sums the three angles and verifies if they satisfy the triangle sum condition of 180 degrees.

3. Importance of Triangle Sum

Details: Understanding the triangle sum is crucial for solving geometric problems, proving triangle congruence, and determining unknown angles in triangles.

4. Using the Calculator

Tips: Enter all three angles in degrees. Each angle must be between 0 and 180 degrees. The calculator will verify if they can form a valid triangle.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all types of triangles?
A: Yes, the sum of interior angles is always 180° for any triangle, regardless of type.

Q2: What if my angles don't sum to 180°?
A: Then they cannot form a valid triangle. Check your angle measurements.

Q3: Can I find a missing angle if I know two angles?
A: Yes, subtract the sum of the known angles from 180° to find the missing angle.

Q4: Does this apply to triangles on curved surfaces?
A: No, this theorem only applies to Euclidean (flat) geometry. On curved surfaces, triangle sums can be greater or less than 180°.

Q5: How is this used in real-world applications?
A: It's used in architecture, engineering, navigation, and computer graphics where triangular calculations are needed.