Question

question
find the value of x, y, and z in the rhombus below.
answer
attempt 1 out of 2
x =
y =
z =
9.3-9.4 rhombi and squares
due: december 3 at 11:00 am
grade: 56%
parallelagram / rhombus properties, sides and angles
parallelagram / rhombus properties, sides and angles (algebraic)
quadrilateral properties, diagonals
scientific calculator
graphing calculator
deltamath
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Explanation:

Step1: Use rhombus adjacent angles property

Adjacent angles in a rhombus are supplementary. So $2x + 10 + 88 = 180$.
$2x + 98 = 180$ → $2x = 82$ → $x = 41$.

Step2: Use rhombus opposite angles property

Opposite angles in a rhombus are equal. So $-3y - 2 = 88$.
$-3y = 90$ → $y = -30$.

Step3: Use rhombus opposite angles property

Opposite angles in a rhombus are equal. So $-6z + 2 = 2x + 10$. Substitute $x=41$:
$-6z + 2 = 2(41) + 10 = 92$ → $-6z = 90$ → $z = -15$.

Answer:

$x = 41$
$y = -30$
$z = -15$