)the figure below shows parallel lines cut by a transversal:
a pair of parallel lines is shown, cut by a transversal. angle 1 is located in the upper right exterior corner on the top line, and angle 2 is located in the upper right corner of the bottom line.
which statement is true about ∠1 and ∠2?
1 and 2 are complementary because they are a pair of corresponding angles
1 and 2 are congruent because they are a pair of corresponding angles
1 and 2 are complementary because they are a pair of alternate interior angles
1 and 2 are congruent because they are a pair of alternate interior angles

1 and 2 are congruent because they are a pair of corresponding angles

true

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.