91Ó°ÊÓ

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

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

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

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

$∠BAC$and $∠ACD$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.

$\begin{array}{c}∠BACâ‰\dots ∠ACD\\ m∠BAC=m∠ACD\\ x=56\end{array}$

Thus,$x=56$

$∠DAB$and $∠ABC$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.

$m∠DAB+m∠ABC=180$

$24+x+y=180$

$24+56+y=180$

$y=180−80$

$y=100$

Thus, $y=100$

$∠DAB$and $∠CDA$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.

$m∠DAB+m∠CDA=180$

$24+x+4z=180$

$24+56+4z=180$

$4z=180−80$

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

$z=25$

Thus, $z=25$