Exterior Angle Calculator Form
Choose a mode, enter values, and calculate geometry measures instantly.
Example Data Table
| Shape or Case | Known Value | Formula | Exterior Angle |
|---|---|---|---|
| Regular pentagon | n = 5 | 360 / n | 72° |
| Regular hexagon | n = 6 | 360 / n | 60° |
| Interior angle known | Interior = 135° | 180 - interior | 45° |
| Triangle remote angles | 55°, 70° | a + b | 125° |
Formula Used
Exterior angle rules depend on the geometry case. For a regular polygon, each exterior angle equals 360° divided by the number of sides.
When an interior angle is known, the exterior angle equals 180° minus the interior angle because they form a linear pair.
For a triangle, one exterior angle equals the sum of the two remote interior angles. This gives a quick check for triangle angle relationships.
If you know the exterior angle and total turns, the required count equals 360° multiplied by turns, then divided by the angle size.
- Regular polygon: Exterior = 360 / n
- Interior to exterior: Exterior = 180 - Interior
- Triangle exterior: Exterior = Remote A + Remote B
- Count from turns: Count = (360 × Turns) / Exterior
How to Use This Calculator
- Select the calculation mode that matches your problem.
- Enter the known values, such as sides, interior angle, or remote angles.
- Choose the number of decimal places for rounded output.
- Press the calculate button to display results below the header.
- Review supporting values like interior sums and polygon checks.
- Use the CSV or PDF buttons to save the current result set.
This layout supports large, small, and mobile screens. The input cards automatically flow across three, two, or one columns.
Frequently Asked Questions
1. What is an exterior angle?
An exterior angle is formed outside a polygon when one side is extended. It usually pairs with the adjacent interior angle to make 180 degrees.
2. Why do regular polygon exterior angles sum to 360°?
Walking around a polygon makes one complete turn. That full turning motion equals 360 degrees, so all exterior angles together always total 360 degrees.
3. How do I find an exterior angle from an interior angle?
Subtract the interior angle from 180 degrees. The two angles form a straight line, so their measures are supplementary.
4. Can this calculator handle triangles?
Yes. Use the triangle mode when two remote interior angles are known. Their sum equals the exterior angle at the remaining vertex.
5. What if the polygon is irregular?
The regular polygon formula gives equal exterior angles only for regular shapes. Irregular polygons may have different exterior angles, though their total still equals 360 degrees.
6. Why does the polygon count sometimes show decimals?
A decimal count means the given exterior angle does not produce a whole-sided polygon for the selected total turns. Whole numbers are needed for standard polygons.
7. Does rounding affect geometry checks?
Rounding changes only the displayed values. Internal calculations still follow the entered numbers, so small display differences may appear at lower precision settings.
8. Can I save my results for reports?
Yes. Use the built-in CSV export for data tables and the PDF button for a printable document version of the current page results.