For any pair of angles formed
by a transversal intersecting parallel lines,
what are two possible relationships?

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)

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation: