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a circle is divided into 10 sectors.the sizes of angles are in ap, the angle of largest sector is seven times angle in small sector. find small sector

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Anonymous
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  1. so the angles are:
    a, a+d, a+2d, ... , a+9d

    a+9d = 7a
    9d = 6a
    d = 2a/3

    also sum of the 10 terms = 360
    (10/2)(2a + 9d) = 360
    2a + 9d = 72
    sub in other value:
    2a + 9(2a/3) = 72
    6a + 18a = 216
    a = 9
    then d = 18/3 = 6

    the angle of the small sector is 9°

    check:
    terms are 9, 15, 21, .... , 63
    the last term is 7 times the first? , Check!
    sum of terms = 5(first + last) = 5(9+63) = 360, Check!

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    Reiny

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