91Ó°ÊÓ

Arrowheads denotes line segment $\stackrel{¯}{AB}$, $\stackrel{¯}{CD}$, and $\stackrel{¯}{EF}$are parallel

Line segment $\stackrel{¯}{AC}$is transversal to the parallel lines $\stackrel{¯}{AB},\stackrel{¯}{CD}$,

Line segment $\stackrel{¯}{CE}$is transversal to the parallel lines $\stackrel{¯}{CD}$,$\stackrel{¯}{EF}$

$∠DCA$and $∠CAB$forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

$m∠DCA+m∠CAB=180$

$2x+y+120=180$

$2x+y=180−120$

$2x+y=60\left(1\right)$

$∠DCE$and $∠CEF$forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

role="math" localid="1637760125240" $m∠DCE+m∠CEF=180$

$2x−y+140=180$

$2x−y=180−140$

$2x−y=40\left(2\right)$

$$\begin{gathered} 2x+y=60 \\ \underline{2x-y=40} \\ 4x=100 \\ x=25 \end{gathered}$$

$2\left(25\right)+y=60$

$50+y=60$

$y=60−50$

$y=10$

Thus, $x=25$and$y=10$