Assume that $a\parallel b$and $c\parallel d$, name all angels supplementary to $\angle 2$.

• $a$is transversal to parallel lines$c$and$d$
• $b$is transversal to parallel lines$c$and$d$
• $c$is transversal to parallel lines $a$and role="math" localid="1637668529774" $b$
• $d$is transversal to parallel lines $a$and$b$

Since, $\angle 1$and $\angle 2$form a linear pair.

So, $\angle 1$is supplementary to$\angle 2$

All angles congruent to $\angle 1$are also supplementary to$\angle 2$

Corresponding angle to $\angle 1$is $\angle 3$and $\angle 9$

Corresponding angle to $\angle 3$is$\angle 11$

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

Thus,$\angle 1\cong \angle 3,\angle 1\cong \angle 9,\text{and}\angle 3\cong \angle 11$

Vertically opposite angle to $\angle 1$is$\angle 6$

Vertically opposite angle to role="math" localid="1637668870317" $\angle 3$is $\angle 8$

Vertically opposite angle to $\angle 9$is$\angle 14$

Vertically opposite angle to $\angle 11$is$\angle 16$

Theorem 2-3: Vertically opposite angles are congruent, so

$\angle 1\cong \angle 6,\angle 3\cong \angle 8,\angle 9\cong \angle 14,\text{and}\angle 11\cong \angle 16$