91Ó°ÊÓ

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

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

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

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

$∠SPQ$ and $∠PQR$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.

$m∠SPQ+m∠PQR=180$

$110+x=180$

$x=180−110$

$x=70$

$∠PQR$and $∠SRD$forms a pair of corresponding angles

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

$m∠SRD=m∠PQR$

$5y+10=x$

$5y+10=70$

$5y=70−10$

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

$y=12$

Thus,$y=12$

$∠USB$and $∠SRD$forms a pair of corresponding angles

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

$m∠PQR=m∠SRD$

$z+32=5y+10$

$z=5\left(12\right)+10−32$

$z=60−22$

$z=38$

Thus,$z=38$