Find the values of $x,y$and $z$

Arrowheads denotes line segment $\overline{AB}$is parallel to$\overline{CD}$

Double arrowheads denotes line segment $\overline{XY}$is parallel to $\overline{UV}$

Line segments $\overline{XY}\text{and}\overline{UV}$are transversal to the parallel lines $\overline{AB}$and$\overline{CD}$

Line segments $\overline{AB}\text{and}\overline{CD}$are transversal to the parallel lines $\overline{XY}$and$\overline{UV}$

$\angle SPQ$ and $\angle PQR$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.

$m\angle SPQ+m\angle PQR=180$

$110+x=180$

$x=180-110$

$x=70$

$\angle PQR$and $\angle SRD$forms a pair of corresponding angles

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

$m\angle SRD=m\angle PQR$

$5y+10=x$

$5y+10=70$

$5y=70-10$

$y=\frac{60}{5}$

$y=12$

Thus,$y=12$

$\angle USB$and $\angle SRD$forms a pair of corresponding angles

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

$m\angle PQR=m\angle SRD$

$z+32=5y+10$

$z=5\left(12\right)+10-32$

$z=60-22$

$z=38$

Thus,$z=38$