find the value of $x$, $y$, and $z$ in the parallelogram below.

Question

Accepted Answer

# Explanation:
## Step1: Use property of opposite angles in parallelogram
In a parallelogram, opposite angles are equal.
So, $4x - 9=101$
$$
\begin{align*}
4x&=101 + 9\
4x&=110\
x&=\frac{110}{4}=27.5
\end{align*}
$$
## Step2: Use property of consecutive angles in parallelogram
Consecutive angles in a parallelogram are supplementary.
$(2y + 1)+101=180$
$$
\begin{align*}
2y+1&=180 - 101\
2y+1&=79\
2y&=79 - 1\
2y&=78\
y&=39
\end{align*}
$$
## Step3: Substitute $y = 39$ into $4z+y$
Since $4z + y=2y + 1$ (opposite angles are equal)
Substitute $y = 39$
$4z+39=2\times39 + 1$
$$
\begin{align*}
4z+39&=78 + 1\
4z+39&=79\
4z&=79 - 39\
4z&=40\
z&=10
\end{align*}
$$

# Answer:
$x = 27.5$, $y = 39$, $z = 10$

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Question

Explanation:

Step1: Use property of opposite angles in parallelogram

Step2: Use property of consecutive angles in parallelogram

Step3: Substitute \(y = 39\) into \(4z+y\)

Answer: