Question

find the value of ( x ), ( y ), and ( z ), in the rhombus below.
answer
( x=quad y=quad z=quad )

Explanation:

Step1: Recall properties of a rhombus

In a rhombus, all four sides are equal in length. So we can set the expressions for the sides equal to each other.

First, let's find the value of \( x \). One side is given as \( 8 \) and another side is \( -x - 6 \). Since all sides of a rhombus are equal, we have the equation:
\( -x - 6 = 8 \)

To solve for \( x \), we add \( 6 \) to both sides:
\( -x = 8 + 6 \)
\( -x = 14 \)

Then multiply both sides by \( -1 \):
\( x = -14 \)

Step2: Find the value of \( y \)

One side is \( 8 \) and another side is \( -5y + 3 \). Setting them equal (because all sides of a rhombus are equal):
\( -5y + 3 = 8 \)

Subtract \( 3 \) from both sides:
\( -5y = 8 - 3 \)
\( -5y = 5 \)

Divide both sides by \( -5 \):
\( y = \frac{5}{-5} \)
\( y = -1 \)

Step3: Find the value of \( z \)

One side is \( 8 \) and another side is \( -8z + 8 \). Setting them equal:
\( -8z + 8 = 8 \)

Subtract \( 8 \) from both sides:
\( -8z = 8 - 8 \)
\( -8z = 0 \)

Divide both sides by \( -8 \):
\( z = \frac{0}{-8} \)
\( z = 0 \)

Answer:

\( x = -14 \), \( y = -1 \), \( z = 0 \)