1. What is an Exterior Angle?

An exterior angle of a polygon is the angle formed between one side of the polygon and the extension of an adjacent side. For any regular polygon (where all sides and angles are equal), all exterior angles are equal and sum up to 360°.

2. How the Calculator Works

The calculator uses the exterior angle formula:

Where:

• \( n \) — Number of sides of the regular polygon
• 360° — Sum of all exterior angles of any polygon

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

3. Properties of Exterior Angles

Key Properties:

• The sum of exterior angles is always 360° for any polygon
• In a regular polygon, all exterior angles are equal
• The exterior angle and interior angle are supplementary (add up to 180°)
• As the number of sides increases, each exterior angle decreases

4. Using the Calculator

Instructions: Simply enter the number of sides (must be 3 or greater) of your regular polygon and click calculate to find the measure of each exterior angle.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for irregular polygons?
A: No, this calculator is for regular polygons only. Irregular polygons can have exterior angles of different measures.

Q2: What's the smallest possible exterior angle?
A: As the number of sides approaches infinity (like a circle), the exterior angle approaches 0°.

Q3: How is this related to interior angles?
A: For any regular polygon: Interior Angle = 180° - Exterior Angle.

Q4: What's the exterior angle of an equilateral triangle?
A: 120° (360° ÷ 3 sides).

Q5: Can a polygon have 2 sides?
A: No, a polygon must have at least 3 sides (triangle).