1. What is the Exterior Angle Formula?

Definition: This formula calculates the measure of an exterior angle of a regular polygon.

Purpose: It helps in geometry to determine the angle formed by one side of a polygon and the extension of an adjacent side.

2. How Does the Formula Work?

The formula is:

Where:

• \( n \) — Number of sides in the regular polygon (must be ≥ 3)

Explanation: The sum of all exterior angles of any polygon is always 360°, so dividing by the number of sides gives each exterior angle.

3. Importance of Exterior Angles

Details: Exterior angles are crucial in polygon analysis, architectural design, and various engineering applications.

4. Using the Calculator

Tips: Enter the number of sides (minimum 3) of your regular polygon. The calculator will compute the measure of each exterior angle.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for irregular polygons?
A: No, this formula only applies to regular polygons where all sides and angles are equal.

Q2: What's the smallest number of sides allowed?
A: The minimum is 3 sides (a triangle).

Q3: How is this related to interior angles?
A: For any polygon, interior angle + exterior angle = 180° at each vertex.

Q4: Can I use this for star polygons?
A: No, this formula is specifically for simple, convex regular polygons.

Q5: Why is the sum always 360°?
A: This is a fundamental property of polygons - completing a full rotation around the shape.