1. What is the Exterior Angle Formula?

The exterior angle formula calculates the measure of each exterior angle of a regular polygon. For any regular polygon with n sides, the exterior angle is equal to 360 degrees divided by the number of sides.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

Where:

• \( n \) — Number of sides of the regular polygon
• \( 360^\circ \) — Total degrees in a full rotation

Explanation: The sum of all exterior angles of any convex polygon is always 360 degrees. For a regular polygon, all exterior angles are equal.

3. Importance of Exterior Angle Calculation

Details: Calculating exterior angles is fundamental in geometry for understanding polygon properties, architectural design, and various engineering applications.

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 exterior angle.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the relationship between interior and exterior angles?
A: For any polygon, interior angle + exterior angle = 180 degrees at each vertex.

Q3: What is the minimum number of sides for a polygon?
A: A polygon must have at least 3 sides (triangle). The calculator requires n ≥ 3.

Q4: Can exterior angles be greater than 180 degrees?
A: For convex polygons, exterior angles are always less than 180 degrees. Concave polygons can have exterior angles greater than 180 degrees.

Q5: How is this used in real-world applications?
A: Exterior angle calculations are used in architecture, computer graphics, surveying, and various engineering fields involving geometric design.