1. What is the Exterior Angle of a Polygon?

The exterior angle of a regular polygon is the angle formed between any side of the polygon and the extension of its adjacent side. In a regular polygon, all exterior angles are equal.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

Where:

• \( n \) — Number of sides of the regular polygon
• \( 360^\circ \) — Sum of all exterior angles of any convex polygon

Explanation: The sum of all exterior angles of any convex polygon is always 360 degrees. For a regular polygon with n sides, each exterior angle is equal to 360 divided by n.

3. Importance of Exterior Angle Calculation

Details: Calculating exterior angles is fundamental in geometry for understanding polygon properties, architectural design, and various engineering applications where angular measurements are crucial.

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 all polygons?
A: This formula works specifically for regular polygons where all sides and angles are equal. For irregular polygons, exterior angles may vary.

Q2: 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.

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

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 is the sum of exterior angles always 360°?
A: This is a fundamental property of polygons - if you travel around the polygon, the total turn (sum of exterior angles) is always 360°.