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

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

Line segment $\overline{EF}$is transversal to the parallel lines

Line segment $\overline{GH}$is perpendicular to the parallel lines

$\angle BQR$ and $\angle QRD$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.

$m\angle BQR+m\angle QRD=180$

$3x+90=180$

$3x=180-90$

$x=\frac{90}{3}$

$x=30$

Thus, $x=30$

$\angle APE$and $\angle CRP$forms a pair of corresponding angles

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

$m\angle CRP=m\angle APE$

$8y+4=68$

$8y=68-4$

$y=\frac{64}{8}$

$y=8$

Thus$y=8$

$\overline{GH}$is perpendicular to $\overline{CD}$

$m\angle CRQ=90$

$8y+4+2z=90$

$2z=90-4-8\left(8\right)$

$2z=86-68$

$z=\frac{22}{2}$

$z=11$

Thus $z=11$