What This Calculator Does
This tool calculates the sum of the interior angles of any simple polygon based on its number of sides. A polygon's interior angles always add up to a fixed total that depends only on how many sides it has — not on its shape or size. Enter the number of sides and you instantly get the total, plus the measure of each angle if the polygon is regular (all sides and angles equal).
The Formula
The sum of interior angles is given by:
Here n is the number of sides. The logic: any convex polygon can be split into (n - 2) triangles, and each triangle's angles sum to 180^\circ. For a regular polygon, each interior angle equals S ÷ n. The exterior angles of any convex polygon always sum to 360^\circ, so each exterior angle of a regular polygon is 360^\circ ÷ n.
How to Use It
Type the number of sides (must be 3 or more) and read the results. For example, a pentagon has 5 sides.
Worked Example
For a hexagon, n = 6. Sum of interior angles =
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