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13 June, 05:54

What is the sum of the interior angles, each interior angle, the central angle, and each exterior angle of a pentagon, a hexagon, an octogon, a nonagon, a decagon and a dodecagon.

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  1. 13 June, 09:34
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    Sum of Interior Angles: Formula: (n-2) * 180

    -Pentagon: 540 °

    -Hexagon: 720 °

    -Octagon: 900 °

    -Nonagon: 1260 °

    -Decagon: 1440 °

    -Dodecagon: 1800 °

    Each interior Angle: Formula: [ (n-2) * 180] / n

    -Pentagon: 108°

    -Hexagon: 120°

    -Octagon: 135°

    -Nonagon: 140°

    -Decagon: 144°

    -Dodecagon: 150°

    The sum of the exterior angles of each polygon stated above is equal to 360 degrees. Using the formula: (180-interior angle) * n

    The central angle is formed by making a circle in the middle and divide it by the number of sides. Therefore, CA = 360 / n

    -Pentagon: 72°

    -Hexagon: 60°

    -Octagon: 45°

    -Nonagon: 40°

    -Decagon: 36°

    -Dodecagon: 30°
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