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Math Help - Counting

  1. #1
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    Counting

    How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?


    Vicky.

    Thanks.
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  2. #2
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    Hello, Vicky!

    How many pairs of vertical angles are formed by five distinct lines
    that have a common point of intersection?
    Code:
                      *
              *   J   *   A   *
               *      *      *
                *     *     *
            I    *    *    *    B
      *           *   *   *           *
          *        *  *  *        *
              *     * * *     *
                  *  ***  *
           H          *           C
                  *  ***  *
              *     * * *     *
          *        *  *  *        *
      *           *   *   *           *
            G    *    *    *    D
                *     *     *
               *      *      *
              *   F   *   E   *
                      *
    I found twenty pairs.

    In the list below, A means \angle A
    . . and AB means A+B.


    . . . . . . . . . . . . (A|F),\;(B|G),\;(C|H),\;(D|I),\;(E|J)

    . . . . . . . . (AB|FG),\;(BC|GH),\;(CD|HI),\;(DE|IJ),\;(EF|JA)

    . . . . (ABC|FGH),\;(BCD|GHI),\;(CDE|HIJ),\;(D{E}F|IJA),\;  (EFG|JAB)

    (ABCD|FGHI),\;(BCDE|GHIJ),\;(CD{E}F|HIJA),\;(D{E}F  G|IJAB), \;(EFGH|JABC)

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  3. #3
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    Thank You!!!!!!!!!!!!!!!!!!!!

    Vicky.
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