1. ## geometry problems

in attachments

2. Hello, dgenerationx2!

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

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

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

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

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

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

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