1. What is the Exterior Angle Formula?

The exterior angle formula calculates the angle formed outside a regular polygon when one side is extended. For any regular polygon, the sum of all exterior angles is always 360 degrees.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

Where:

• \( E \) — Exterior angle (degrees)
• \( n \) — Number of sides in the regular polygon

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

3. Importance of Exterior Angle Calculation

Details: Calculating exterior angles is essential in geometry for understanding polygon properties, architectural design, and various engineering applications where regular shapes are used.

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 in degrees.

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. Irregular polygons have varying exterior angles.

Q2: What is the minimum number of sides required?
A: The minimum number of sides is 3 (triangle). Polygons must have at least 3 sides to be valid.

Q3: How are interior and exterior angles related?
A: For any polygon, the interior and exterior angles at the same vertex are supplementary (add up to 180 degrees).

Q4: Why is the sum of exterior angles always 360 degrees?
A: This is a fundamental property of polygons - if you travel around the polygon, you make one complete turn (360 degrees).

Q5: Can this calculator handle decimal inputs?
A: The calculator requires whole numbers for sides since polygons must have an integer number of sides.