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Math Help - geometry problems

  1. #1
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    geometry problems

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  2. #2
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    Hello, dgenerationx2!

    Given: rhombus ABCD,\;\angle BCD = 110^o
    Code:
              A * - - - - - - - - * B
               /  *           *  /
              /     * E   *     /
             /        *        /
            /     *     *     /
           /  *           *  /
        D * - - - - - - - - * C

    1)\;\angle DEA = ?\qquad (A)\;70^o \qquad(B)\;100^o\qquad(C)\;90^o\qquad(D)\;80^o
    The diagonals of a rhombus are perpendicular: . \angle DEA = 90^o .[C]


    2)\;\angle DAE = ?\qquad(A)\;45^o\qquad(B)\;55^o\qquad(C)\;50^o\qqu  ad(D)\;35^o
    \angle DAB = 100^o . . . Opposite angles of a parallelogram are equal.

    The diagonals of a rhombus bisect the vertex angles.
    . . Therefore: . \angle DAE = 55^o .[B}



    3)\;\angle DCE = ?\qquad (A)\;40^o\qquad(B)\;55^o\quad(C)\;50^o\qquad(D)\;3  5^o
    \Delta ADC is an isosceles triangle.
    . . Therefore: . \angle DCE \,=\,\angle DAE \,=\,55^o .[B]


    4)\;\angle CBE = ?\qquad (A)\;35^o\qquad(B)\;40^o\qquad(C)\;55^o\qquad (D)\;50^o
    \angle ABC = 70^o . . . Adjacent angles of a parellelogram are supplementary.

    The diagonals of a rhombus bisect the vertex angles.
    . . Therefore: . \angle CBE \,=\,35^o .[A]


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