What is the formula for the sum of the interior angles of a polygon

         Sum of the interior angles = (n - 2) × 180°.

         Where n is the number of sides of the polygon.

Explanation:

The formula (n - 2) × 180° is valid for any convex polygon.

A convex polygon is one whose interior angles (every interior angle) measure less than 180°.

You can prove and remember that formula following this reasoning:

For example, for a pentagon, a polygon with 5 sides, you can can draw 5 - 2 = 3 diagonals from one vertex, and so obtain 3 triangles. Then the sum of the interior angles shall be (n - 2) × 180° = (5 - 2) × 180° = 3 × 180° = 540°.

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