Calculator Form
Choose one method and calculate the exterior angle of a regular polygon.
Example Data Table
These examples help verify common regular polygon exterior angles.
| Polygon | Sides | Exterior Angle | Interior Angle | Central Angle |
|---|---|---|---|---|
| Triangle | 3 | 120° | 60° | 120° |
| Square | 4 | 90° | 90° | 90° |
| Pentagon | 5 | 72° | 108° | 72° |
| Hexagon | 6 | 60° | 120° | 60° |
| Decagon | 10 | 36° | 144° | 36° |
Formula Used
Each exterior angle = 360° / n
Each exterior angle = 180° − interior angle
n = 360° / exterior angle
Interior angle = 180° − exterior angle
These formulas apply to regular polygons, where all sides and angles are equal. The sum of one exterior angle at every vertex is always 360°.
How to Use This Calculator
- Select a method based on your known value.
- Enter the number of sides, interior angle, or exterior angle.
- Choose your preferred decimal precision.
- Click the calculate button.
- Read the result summary above the form.
- Review the detailed steps and verification metrics.
- Inspect the graph to understand cumulative turning.
- Export the result table as CSV or PDF.
FAQs
1. What is an exterior angle in a polygon?
An exterior angle forms outside the polygon when one side extends. In a regular polygon, every exterior angle has the same measure.
2. How do I find the exterior angle from sides?
Divide 360° by the number of sides. For example, a regular hexagon has 360° ÷ 6 = 60° exterior angles.
3. Why do all exterior angles add to 360°?
Walking around a polygon makes one full turn. A full turn equals 360°, so the sum of one exterior angle at every vertex is always 360°.
4. Can this calculator work for irregular polygons?
This calculator is designed for regular polygons. Irregular polygons can have different exterior angles, so one single formula does not describe every vertex.
5. What is the relationship between interior and exterior angles?
For a regular polygon, each interior and exterior angle are supplementary. Their measures always add to 180°.
6. Is the central angle equal to the exterior angle?
Yes, in a regular polygon the central angle equals the exterior angle. Both are found by dividing 360° by the number of sides.
7. What happens if the angle gives a non-integer side count?
The calculator still shows the theoretical result. It also warns that the value does not match a standard regular polygon with whole-number sides.
8. Why export results as CSV or PDF?
Exports help with homework records, class notes, quick reporting, and checking geometry examples later without recalculating every value.