1. What is Polygon Exterior Angle?

The exterior angle of a polygon is the angle formed between any side of the polygon and the extension of its adjacent side. For any regular polygon, all exterior angles are equal and sum to 360 degrees.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

Where:

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

Explanation: The formula divides the full 360-degree rotation around a point equally among all exterior angles of the polygon.

3. Importance of Exterior Angle Calculation

Details: Calculating exterior angles is essential in geometry for polygon analysis, construction, and design. It helps determine polygon properties and is fundamental in various mathematical and engineering applications.

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

Q2: Do all polygons have equal exterior angles?
A: Only regular polygons (all sides and angles equal) have equal exterior angles. For irregular polygons, exterior angles may vary.

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

Q4: Can exterior angles be greater than 180°?
A: In convex polygons, exterior angles are always less than 180°. In concave polygons, exterior angles can be greater than 180°.

Q5: Why do exterior angles always sum to 360°?
A: This is a fundamental property of polygons - as you travel around the polygon, you make one complete rotation (360°).