91Ó°ÊÓ

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 $∠DAB$and $∠ABC$so,

$∠DAB=∠ABC$

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 $∠EAD$and $∠ACB$so,

$∠EAD=∠ACB$

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 $20°$.