91Ó°ÊÓ

According to the provided information, the opposite sides of the provided figure are parallel. That is $\stackrel{¯}{AB}âˆ\yen \stackrel{¯}{CD}$and $\stackrel{¯}{AD}âˆ\yen \stackrel{¯}{BC}$.

Now, lines$\stackrel{¯}{AD}âˆ\yen \stackrel{¯}{BC}$ and$\stackrel{¯}{AB}$ is a transversal, so by postulate 10 which states that two angles represent the corresponding angles only when a separate line travels through these two lines which are having a parallel relation between them.

Write the corresponding angles.

$∠xâ‰\dots ∠DAB$

That is,$∠x=∠DAB=65°$

Also since ABCD is a parallelogram, so by theorem 5-2 which states that the relationship between two angles that are related to a parallelogram and positioned on the opposite sides of each other is congruent.

Write the opposite angles of provided figure.

$∠yâ‰\dots ∠DAB$

That is,$∠y=∠DAB=65°$

Now, lines$\stackrel{¯}{AB}âˆ\yen \stackrel{¯}{CD}$ and$\stackrel{¯}{AD}$ is a transversal, so by theorem 3-3 which states that relationship between two angles is supplementary when these angles are positioned on the same side of the interior of two lines which are having a separate line that is travelling through them,

Write the supplementary angles.

$∠ADC+∠DAB=180°$

$\begin{array}{c}z+65°=180°\\ z=180°−65°\\ z=115°\end{array}$