91Ó°ÊÓ

• $a$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, $∠1$and $∠2$form a linear pair.

So, $∠1$is supplementary to$∠2$

All angles congruent to $∠1$are also supplementary to$∠2$

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

Corresponding angle to $∠3$is$∠11$

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

Thus,$∠1â‰\dots ∠3,∠1â‰\dots ∠9,\text{and}∠3â‰\dots ∠11$

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

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

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

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

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

$∠1â‰\dots ∠6,∠3â‰\dots ∠8,∠9â‰\dots ∠14,\text{and}∠11â‰\dots ∠16$