Question

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

Short answer

The value that represent x is $50°$and the value that represent y is $20°$.

Step-by-step solution

Step 1. Determine the equation that represents the equation of x

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.

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

Step 2. Determine the equation that represents the difference of x and y

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.

$30°=\left(x-y\right)°$

$\left(x-y\right)°=30°$

Step 3. By using the obtained equations determine the value of x and y

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

Step 4. Make the conclusion

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