UNDERSTANDING SHAPES (Including Polygons)

165. The Regular Polygon's Secret · Angles, sides, and the magic of n

Exterior + Interior = 180°, and sum of all exterior angles = 360°.

OVVₙ₋₁V₁Exterior Angle = 360°/nInterior Angle = 180° − 360°/n312← sides (n) →360° ÷ 6 = 60°360° ÷ 6 = 60°180° − 360° ÷ 6 = 120°180° − 360° ÷ 6 = 120°n = 6n = 6Vn
This diagram shows a regular n-sided polygon inscribed in a circle. • Drag vertex V to change the polygon's size and rotation • Drag the green slider to change the number of sides (n) • Each exterior angle = 360° ÷ n (purple arc) • Each interior angle = 180° − 360°/n (yellow arc) • Together they form a linear pair — always adding to 180°. For a regular hexagon (n = 6): exterior = 60°, interior = 120°. For a regular decagon (n = 10): exterior = 36°, interior = 144°.
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