Polygon Interior Angles Calculator
Find a missing interior angle or check a complete polygon angle list. Choose convex-only angles or allow reflex angles in a simple concave polygon.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
A simple polygon can be triangulated into n−2 triangles, so its interior angles total(n−2)×180°. Subtract the known angles for one missing value, or compare the entire sum with that target.
Interior-angle sum=(n−2)×180°
Worked example
A pentagon totals540°. Given90°,110°,120° and100°, the missing angle is120°.
Assumptions and input details
Use3–100 sides. Missing-angle mode needs exactlyn−1 entries; check mode needsn. Angles accept fractions/six-place decimals within±1e6 and denominators≤1e6. Convex angles lie strictly between0° and180°. Simple-polygon mode allows reflex angles below360°, except triangles still require angles below180°. Matching the sum is a necessary condition and does not prove that an arbitrary ordered list forms the intended nonintersecting polygon.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Angle sums, missing angles and range checks use exact fractions.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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