The Angle Sum Shortcut for Polygons
Tired of memorizing angle sums for every polygon? There's a simple formula that works for ALL of them!
Subject: geometry • Classes: 6–12 • Difficulty: intermediate (9-10)
The Trick
The sum of the interior angles of any polygon with $n$ sides is given by the formula: $(n-2) \times 180^{\circ}$. This works because you can always divide any polygon into $(n-2)$ triangles, and each triangle has an angle sum of $180^{\circ}$. Therefore, the total angle sum of the polygon is just the sum of the angles of all those triangles.
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