1. What is the Internal Angle Formula?

The internal 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 internal angle formula:

Where:

• \( I \) — Internal angle in degrees
• \( n \) — Number of sides in the polygon

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 Internal Angle Calculation

Details: Calculating internal angles is essential in geometry, architecture, engineering, and design. It helps in constructing regular polygons, understanding geometric properties, and solving various mathematical problems.

4. Using the Calculator

Tips: Enter the number of sides (must be 3 or greater) of the regular polygon. The calculator will compute the measure of each internal angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular polygon?
A: A regular polygon is a polygon where all sides are equal in length and all internal angles are equal in measure.

Q2: 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.

Q3: Does this formula work for irregular polygons?
A: No, this formula calculates the measure of each internal angle in a regular polygon where all angles are equal.

Q4: What are some common polygon internal angles?
A: Triangle: 60°, Square: 90°, Pentagon: 108°, Hexagon: 120°, Heptagon: ≈128.57°, Octagon: 135°.

Q5: How is this formula derived?
A: The formula is derived from the fact that the sum of interior angles of an n-sided polygon is (n-2) × 180°, divided equally among n angles in a regular polygon.