trig

the angle in one regular polygon is to that in another as 3:2 and the number of the sides in first is twice that in second determine the the number of sides of 2 polygons

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  1. let the number of sides of the second be n
    then the number of sides of the first is 2n

    size of angle of the second = 180(n-2)/n
    size of angle of the first = 180(2n-2)/(2n)

    but that ratio is 3:2

    [180(n-2)/n] / [180(2n-2)/(2n)] = 2/3
    after some canceling and cross-multiplying ...
    n = 4

    one polygon is a square , the other is an octogon

    check:
    (4 sides and 8 sides)
    each angle in a square is 90°, each angle in an octogon is 135°
    135 : 90 = 3 : 2

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