1. What is the Polygon Interior Angle Formula?

The polygon interior angle formula calculates the measure of each interior angle in a regular polygon. It is derived from the fact that the sum of all interior angles in an n-sided polygon is (n-2) × 180 degrees.

2. How Does the Calculator Work?

The calculator uses the interior angle formula:

Where:

• \( I \) — Interior angle (degrees)
• \( n \) — Number of sides

Explanation: The formula divides the total sum of interior angles by the number of sides to find the measure of each equal angle in a regular polygon.

3. Importance of Interior Angle Calculation

Details: Calculating interior angles is essential in geometry, architecture, engineering, and design for creating and analyzing polygonal shapes and structures.

4. Using the Calculator

Tips: Enter the number of sides (must be 3 or greater). The calculator will compute the interior angle for a regular polygon with that number of sides.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular polygon?
A: A regular polygon has all sides equal in length and all interior angles equal in measure.

Q2: What is the minimum number of sides for a polygon?
A: A polygon must have at least 3 sides (triangle). Two-sided shapes are not considered polygons.

Q3: What are some common polygon interior angles?
A: Triangle: 60°, Square: 90°, Pentagon: 108°, Hexagon: 120°, Heptagon: ≈128.57°, Octagon: 135°.

Q4: Does this formula work for irregular polygons?
A: No, this formula only works for regular polygons where all interior angles are equal. Irregular polygons have varying interior angles.

Q5: What is the relationship between interior and exterior angles?
A: In any polygon, the interior and exterior angles at each vertex are supplementary (add up to 180°).