How this calculation works
The exterior turn is 180° minus the interior angle. A full walk around a convex regular polygon turns through 360°.
n = 360/(180−θ)A worked example
A 150° interior angle corresponds to a 30° exterior turn, so the polygon has 12 sides.
Good to know
The angle must describe a regular polygon with at least three sides.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Recover the integer number of sides implied by the interior angle of a regular polygon.
The primary result is labeled “Sides”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The angle must describe a regular polygon with at least three sides.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
A 150° interior angle corresponds to a 30° exterior turn, so the polygon has 12 sides.
Which rule does this calculator apply?
n = 360/(180−θ)