UNDERSTANDING SHAPES (Including Polygons)

163. The Polygon's Angle Secret · how diagonals unlock the sum of interior angles

The sum of interior angles of the pentagon equals 540° (3×180°). The sum of interior angles of an n-sided polygon is (n − 2) × 180°.

∠A = 54°∠A = 54°∠B = 126°∠B = 126°∠C = 144°∠C = 144°∠D = 144°∠D = 144°∠E = 72°∠E = 72°Sum = 540°Sum = 540°54° + 126° + 144° + 144° + 72° = 540°54° + 126° + 144° + 144° + 72° = 540°ABCDE
The sum of interior angles of an n-sided polygon is (n − 2) × 180°. For a triangle (n=3) it's 180°, quadrilateral (n=4) it's 360°, pentagon (n=5) it's 540°, hexagon (n=6) it's 720°, and so on.
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