Question

find the value of z and y in the parallelogram below.

Explanation:

Step1: Use property of parallelogram - opposite sides are equal

For the side - length relationship:
Set up the equation for the vertical sides: $19=- 10y - 1$.
Solve for $y$:
\[

$$\begin{align*} 19&=-10y - 1\\ 19 + 1&=-10y\\ 20&=-10y\\ y&=- 2 \end{align*}$$

\]

Step2: Use property of parallelogram - opposite sides are equal

Set up the equation for the horizontal sides: $9 = 9z-9$.
Solve for $z$:
\[

$$\begin{align*} 9&=9z - 9\\ 9+9&=9z\\ 18&=9z\\ z&=2 \end{align*}$$

\]

Answer:

$y=-2,z = 2$