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)

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.