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.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

Where:

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

Explanation: The sum of all exterior angles of any polygon always equals 360°. For a regular polygon, dividing this by the number of sides gives each exterior angle.

3. Importance of Exterior Angles

Details: Exterior angles are fundamental in geometry for analyzing polygon properties, architectural design, and various engineering applications. They help determine the shape and symmetry of polygons.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the minimum number of sides a polygon can have?
A: A polygon must have at least 3 sides (triangle). The calculator requires n ≥ 3.

Q2: Does this work for irregular polygons?
A: No, this formula only works for regular polygons where all exterior angles are equal.

Q3: What's the relationship between interior and exterior angles?
A: For any regular polygon, interior + exterior angle = 180° at each vertex.

Q4: What happens as the number of sides increases?
A: The exterior angle decreases, approaching 0° as the polygon becomes more circle-like.

Q5: Can exterior angles be used to classify polygons?
A: Yes, the exterior angle measurement helps determine the type and properties of regular polygons.