The two possible relationships are congruent and supplementary angles
Step-by-step explanation:
see the attached figure to better understand the problem
In the attached figure, line n is a transversal cutting parallel lines l and m
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .
In the figure the pairs of corresponding angles are:
∠1 and ∠5
∠2 and ∠6
∠3 and ∠7
∠4 and ∠8
When the lines are parallel, the corresponding angles are congruent
so
In this problem
∠1 ≅ ∠5
∠2 ≅ ∠6
∠3 ≅ ∠7
∠4 ≅ ∠8
When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.
In the attached figure, the consecutive interior angles are:
∠3 and ∠6
∠4 and ∠5
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
In this problem
∠3+∠6=180°
∠4+∠5=180°
When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles.
In the attached figure, the alternate interior angles are:
∠3 and ∠5
∠4 and ∠6
If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent.
so
In this problem
∠3 ≅∠5
∠4 ≅ ∠6
When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles.
In the attached figure, the alternate exterior angles are:
∠2 and ∠8
∠1 and ∠7
If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent.
so
In this problem
∠2 ≅ ∠8
∠1 ≅ ∠7
therefore
The two possible relationships for any pair of angles formed by a transversal intersecting parallel lines are congruent (corresponding, alternate exterior and alternate interior angles) or supplementary (consecutive interior angles)
