1. What is the Interior Angle Formula?

Definition: This formula calculates the measure of each interior angle in a regular polygon.

Purpose: It helps in geometry problems and design applications where regular polygon angles are needed.

2. How Does the Formula Work?

The formula is:

Where:

• \( \text{angle} \) — Interior angle in degrees
• \( n \) — Number of sides in the regular polygon

Explanation: The formula works by dividing the sum of interior angles by the number of angles (which equals the number of sides).

3. Importance of Interior Angle Calculation

Details: Knowing interior angles is essential for geometric constructions, architectural design, and engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the smallest number of sides allowed?
A: 3 (triangle). Polygons must have at least 3 sides.

Q2: What's the interior angle of a square?
A: 90° (n=4: (4-2)×180/4 = 90°)

Q3: Does this work for irregular polygons?
A: No, this formula only works for regular polygons (equal sides and angles).

Q4: What happens as n increases?
A: The interior angle approaches 180° as the polygon becomes more circle-like.

Q5: How is this related to exterior angles?
A: Interior + Exterior angle = 180° for any regular polygon.