How this calculator works
Triangulating a simple polygon gives an interior angle sum of 180(n - 2) degrees. A regular polygon divides that sum equally between its vertices. Each exterior turning angle is the supplement of the interior angle. Reverse mode checks that the angle implies a whole side count; a rounded angle may need more digits. Star polygons are outside this model.
Formula
Interior α = π - 2π/n; exterior β = 2π/n; sum = (n - 2)π. Reverse: n = 2π/(π - α) or n = 2π/β.
Worked example
An interior angle of 120° leaves an exterior angle of 60°. Dividing 360° by 60° identifies a regular hexagon with six sides and an interior sum of 720°.
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Frequently asked questions
Can I enter an irregular polygon?
Its interior sum still follows the side-count formula if the polygon is simple, but individual interior angles need not match. The individual-angle results here assume regularity.
Why does 100° fail in interior-angle mode?
It implies 360/(180 - 100) = 4.5 sides. A polygon cannot have a fractional side count.
Is the exterior angle the central angle?
For a convex regular polygon they have the same magnitude, 360/n degrees, although they occur at different places in the drawing.