Find the values of x and y that make the lines shown in red parallel.

Mark the segments of the provided figure.

According to the transversal AB the provided parallel lines consist of angles that are having the same measurement which are $\angle DAB$and $\angle ABC$so,

$\angle DAB=\angle ABC$

Substitute the value of these angles and isolate the variable x.

$\begin{array}{c}5y°=2x°\\ x°=\frac{5y°}{2}\end{array}$

According to the transversal EC the provided parallel lines consist of angles that are having the same measurement which are $\angle EAD$and $\angle ACB$so,

$\angle EAD=\angle ACB$

Substitute the value of these angles.

$30°=\left(x-y\right)°$

$\left(x-y\right)°=30°$

Substitute the value of x from $x°=\frac{5y°}{2}$into the equation $\left(x-y\right)°=30°$ and determine the value of y.

$\begin{array}{c}\frac{5y}{2}-y=30\\ \frac{5y-2y}{2}=30\end{array}$

$3y=60$

$y=\frac{60}{3}$

$=20°$

Substitute the value of y into the equation $x°=\frac{5y°}{2}$and determine the value of x.

role="math" localid="1637920472360" $$\begin{gathered} x=\frac{5\left(20°\right)}{2} \\ =50° \end{gathered}$$

The obtained value of x is $50°$ and y is $20°$.