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Easy: Sum of the interior angles
A polygon with n sides splits into n − 2 triangles, so its interior angles add to (n − 2) × 180°. In a regular polygon every angle is the same: divide the sum by n. The exterior angles of any polygon add to 360°, so each exterior angle of a regular polygon is 360° ÷ n, and an interior and exterior angle add to 180°.
Find the angle measure or the number of sides.
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Drawing diagonals from one vertex splits a polygon with n sides into n − 2 triangles, and each triangle's angles add to 180°.
Always 360°, whatever the number of sides. So each exterior angle of a regular polygon is 360° ÷ n, which is the quickest way to find n.
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