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 to 360°.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

Where:

• \( n \) — Number of sides in the regular 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 in a regular polygon.

3. Importance of Exterior Angles

Details: Understanding exterior angles is fundamental in geometry, helping in polygon analysis, tiling problems, and architectural design. They are also used in calculating interior angles and understanding polygon properties.

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 a regular polygon with that number of sides.

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: Do irregular polygons have equal exterior angles?
A: No, only regular polygons (equal sides and angles) have equal exterior angles. This calculator assumes a regular polygon.

Q3: What's the relationship between interior and exterior angles?
A: For any vertex of a polygon, the interior and exterior angles are supplementary (add up to 180°).

Q4: What's the exterior angle of a regular pentagon?
A: 72° (360° ÷ 5 sides). Try entering 5 in the calculator to verify.

Q5: Why is the sum always 360°?
A: If you walk around the polygon, turning at each corner by the exterior angle, you complete a full 360° rotation when you return to your starting point.