1. What is the Interior Angle Sum Formula?

The interior angle sum formula calculates the total of all interior angles in a polygon. For any polygon with n sides, the sum of its interior angles is given by (n-2) × 180 degrees.

2. How Does the Calculator Work?

The calculator uses the interior angle sum formula:

Where:

• \( n \) — Number of sides in the polygon

Explanation: The formula works because any polygon can be divided into (n-2) triangles, and each triangle has an angle sum of 180°.

3. Importance of Interior Angle Calculation

Details: Calculating interior angle sums is fundamental in geometry for determining polygon properties, architectural design, and various engineering applications.

4. Using the Calculator

Tips: Enter the number of sides (must be 3 or greater). The calculator will compute the sum of all interior angles in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the minimum number of sides required?
A: A polygon must have at least 3 sides (triangle). The calculator accepts values of 3 or greater.

Q2: Does this formula work for all polygons?
A: Yes, the formula works for all simple polygons, whether regular or irregular.

Q3: How is this different from exterior angle sum?
A: The sum of exterior angles for any convex polygon is always 360°, regardless of the number of sides.

Q4: What about complex polygons?
A: For complex (self-intersecting) polygons, different formulas may be needed as the standard formula applies to simple polygons.

Q5: Can I calculate individual interior angles with this?
A: For regular polygons (all sides and angles equal), divide the sum by n. For irregular polygons, additional information is needed.