Find the values of $x$and $y$

Arrowheads denotes line segment $\overline{BC}$is parallel to $\overline{AD}$

Double arrowheads denotes line segment $\overline{AB}$is parallel to $\overline{DC}$

Line segments $\overline{BC}\text{,}\overline{AD}\text{and}\overline{AC}$are transversal to the parallel lines $\overline{AB}$androle="math" localid="1637755834952" $\overline{AD}$

Line segments $\overline{CD}\text{,}\overline{AB}\text{and}\overline{AC}$are transversal to the parallel lines role="math" localid="1637755825832" $\overline{BC}$and$\overline{CD}$

$\angle BAC$and $\angle ACD$forms a pair of alternate interior angles

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

$\begin{array}{c}\angle BAC\cong \angle ACD\\ m\angle BAC=m\angle ACD\\ x=56\end{array}$

Thus,$x=56$

$\angle DAB$and $\angle ABC$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.

$m\angle DAB+m\angle ABC=180$

$24+x+y=180$

$24+56+y=180$

$y=180-80$

$y=100$

Thus, $y=100$

$\angle DAB$and $\angle CDA$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.

$m\angle DAB+m\angle CDA=180$

$24+x+4z=180$

$24+56+4z=180$

$4z=180-80$

$z=\frac{100}{4}$

$z=25$

Thus, $z=25$