Polygon Interior Angle Calculator
A polygon is a flat shape with straight sides, like a triangle, square or hexagon. This finds the angles inside and outside a regular polygon, one where all the sides and all the angles are equal.
- Free
- Works offline after your first visit
- Saves on this device
- No sign-up
- Updated
How it works
The inside angles of any polygon add up to (sides minus 2) times 180 degrees. In a regular polygon, divide that total by the number of sides to get each angle.
The outside angles of any polygon add up to 360 degrees, one full turn. In a regular polygon, each outside angle is 360 divided by the number of sides.
Worked example
A polygon with 6 sides has inside angles that add up to 720 degrees. Each inside angle is 120 degrees, and each outside angle is 60 degrees.
Questions
Does this work for irregular shapes?
Only for regular shapes. In an irregular polygon the angles can differ from one another, though the inside total is still the same.
Why do the outside angles always add up to 360?
Walking once around any polygon, you turn through one full circle in total. Each outside angle is one of those turns.
What is the smallest polygon?
A triangle, with three sides. Enter 3 to see its angles.
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