Question

find the value of x, y, and z, in the rhombus below.
answer attempt 1 out of 2
x =
y =
z =

Explanation:

Step1: Recall rhombus property

In a rhombus, all sides are equal. So we set up equations based on equal - side lengths.

Step2: Set up equation for \(x\)

Set \(8=-9x - 10\). Add 10 to both sides: \(8 + 10=-9x-10 + 10\), which gives \(18=-9x\). Divide both sides by \(-9\): \(x=\frac{18}{-9}=-2\).

Step3: Set up equation for \(y\)

Set \(8 = 3y+2\). Subtract 2 from both sides: \(8 - 2=3y+2 - 2\), which gives \(6 = 3y\). Divide both sides by 3: \(y=\frac{6}{3}=2\).

Step4: Set up equation for \(z\)

Set \(8=8z + 8\). Subtract 8 from both sides: \(8-8=8z + 8-8\), which gives \(0 = 8z\). Divide both sides by 8: \(z = 0\).

Answer:

\(x=-2\), \(y = 2\), \(z = 0\)