The Angle Sum Secret of Polygons

Want to know the secret to quickly finding the sum of angles in any polygon, even without memorizing a formula? It's easier than you think!

Subject: geometry • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

To find the sum of interior angles of any polygon, subtract 2 from the number of sides (n), then multiply by 180 degrees. So, the formula is $(n-2) * 180^{\circ}$. Why does this work? Any polygon can be divided into (n-2) triangles by drawing diagonals from one vertex. Each triangle has an angle sum of 180 degrees. Thus, the total angle sum is (n-2) * 180 degrees.

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