1. What is the Exterior Angle Formula?

The exterior angle formula calculates the angle formed between any side of a polygon and the extension of its adjacent side. 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 in degrees
• \( n \) — Number of sides of the polygon

Explanation: This formula divides the full 360 degrees around a point equally among all exterior angles of a regular polygon.

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 angular measurements are critical.

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 is specifically for 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 is 3 sides (triangle). Polygons must have at least 3 sides to form a closed shape.

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

Q4: Can this calculator handle decimal inputs?
A: No, the number of sides must be a whole number since polygons cannot have fractional sides.

Q5: What is the sum of exterior angles for any polygon?
A: The sum of exterior angles for any convex polygon is always 360 degrees, regardless of the number of sides.