geometry

If the ratio of the interior angle to the exterior angle is 5:1 for a regular polygon, find
a. the size of each exterior angle
b. the number of sides of the polygon
c. the sum of the interior angles
d. Name the polygon

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  1. interior: (n-2)180/n
    exterior: 360/n

    (n-2)180/n ÷ 360/n = (n-2)/2 = 5
    n = 8

    a:
    exterior: 45
    interior: 135

    b: n=8

    c: 6(180) = 1080

    d: octagon

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  2. Oops
    n=12

    exterior: 30
    interior: 150

    n=12

    10(180) = 1800

    dodecagon

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  3. The ratio of interior and exterior angle of regular polygon is is 5:1, find the number of diagonals of the regular polygon.

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