1. What is the Interior Angle Sum Formula?

The interior angle sum formula calculates the total sum of all interior angles in a polygon. For any polygon with n sides, the sum of interior angles is given by (n - 2) × 180°. This formula is fundamental in traverse surveying and geometry.

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 derives from dividing the polygon into (n-2) triangles, each having 180° angle sum.

3. Importance of Interior Angle Calculation

Details: Accurate interior angle calculation is crucial for traverse closure in surveying, ensuring measurement accuracy and verifying geometric consistency in polygonal shapes.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the minimum number of sides required?
A: The minimum number of sides is 3 (triangle). The formula works for any polygon with 3 or more sides.

Q2: Does this work for regular and irregular polygons?
A: Yes, the formula applies to both regular and irregular polygons as it calculates the total sum of all interior angles.

Q3: How is this used in traverse surveying?
A: In traverse surveying, the calculated interior angle sum is compared with measured angles to check for closure errors and ensure accuracy.

Q4: What about exterior angles?
A: The sum of exterior angles for any convex polygon is always 360°, regardless of the number of sides.

Q5: Can this calculate individual interior angles?
A: For regular polygons, divide the total sum by n. For irregular polygons, individual angles must be measured separately.