Printable and digital versions of a "Parallel Lines and Transversals" math worksheet.

Final Answer:
Angles 4 and 5 are alternate interior angles.
True or false: Angle 1 and Angle 5 are corresponding angles → False
Angle 2 and 3 are adjacent angles (not a standard angle pair like corresponding/alternate/supplementary — but in context, they are *adjacent*; however, the question asks “which type of angle pair?”, and since they share a vertex and a side but are not on parallel lines together, they are adjacent angles — but many worksheets expect “vertical angles” only if opposite; here, 2 and 3 are on a straight line with Z, so actually ∠2 and ∠3 are adjacent supplementary angles (they form a linear pair). However, based on standard labeling in such diagrams:
- ∠2 and ∠3 are adjacent angles forming a linear pair → so they are supplementary, but the *type of angle pair* is linear pair (or adjacent supplementary). Yet the worksheet likely expects: linear pair or simply supplementary — but the question says “which type of angle pair?”, and common categories are: corresponding, alternate interior, alternate exterior, consecutive interior (same-side interior), vertical, linear pair.

Looking at typical diagram: transversal Z cuts parallels X and Y. Points labeled around intersection: top-left = 1, top-right = 2, bottom-right = 3, bottom-left = 4 (at upper intersection); lower intersection: top-left = 5, top-right = 6, bottom-right = 7, bottom-left = 8.

Then:
- ∠4 and ∠5: inside the parallels, on opposite sides of transversal → alternate interior angles
- ∠1 and ∠5: both top-left positions → same relative position → corresponding angles → so statement “Angle 1 and Angle 5 are corresponding angles” is True
Wait — correction: In standard labeling, if line X is top parallel, line Y bottom parallel, transversal Z slanting down-right:

At top intersection (X & Z):
- Upper left: ∠1
- Upper right: ∠2
- Lower right: ∠3
- Lower left: ∠4

At bottom intersection (Y & Z):
- Upper left: ∠5
- Upper right: ∠6
- Lower right: ∠7
- Lower left: ∠8

Then:
- ∠1 (top-left) and ∠5 (bottom-left) are both on the left side of transversal and above their respective parallels → corresponding angles → True.

- ∠2 and ∠3: at same intersection, adjacent, forming a straight line → they are a linear pair → supplementary, but the *angle pair type* is linear pair (or adjacent angles on a straight line). However, many worksheets accept “adjacent” or “linear pair”. But the question says “which type of angle pair?” — and common answer expected: linear pair.

But the problem also asks: “Name two angles that are congruent to angle 6.”
∠6 is top-right at lower intersection. Corresponding to ∠2 (top-right at upper intersection) → ∠2 ≅ ∠6 (corresponding, parallel lines). Also, vertical angle to ∠6 is ∠8? No: vertical to ∠6 is ∠8? Wait: at lower intersection, ∠5 & ∠7 are vertical, ∠6 & ∠8 are vertical. Yes: ∠6 and ∠8 are vertical → congruent. So two angles congruent to ∠6: ∠2 and ∠8.

Then:
If m∠3 = 123°, find m∠8.
∠3 and ∠7 are corresponding → ∠7 = 123°. ∠7 and ∠8 are adjacent on straight line → supplementary → m∠8 = 180 − 123 = 57°.

If m∠4 = 47°, find m∠6.
∠4 and ∠6 are alternate interior → congruent → m∠6 = 47°.

If m∠2 = 161°, find m∠6.
∠2 and ∠6 are corresponding → m∠6 = 161°.

If m∠7 = 112°, find m∠8.
∠7 and ∠8 are linear pair → m∠8 = 180 − 112 = 68°.

If m∠5 = 71°, find m∠4.
∠5 and ∠4 are alternate interior → congruent → m∠4 = 71°.

So compiling all required answers:

- Angles 4 and 5: alternate interior angles
- True or false: ∠1 and ∠5 are corresponding → True
- Angle 2 and 3: linear pair (or adjacent supplementary) — but standard term in such worksheets: linear pair
- Two angles congruent to ∠6: ∠2 and ∠8
- m∠8 when m∠3 = 123°: 57°
- m∠6 when m∠4 = 47°: 47°
- m∠6 when m∠2 = 161°: 161°
- m∠8 when m∠7 = 112°: 68°
- m∠4 when m∠5 = 71°: 71°

But the user only asked for the final answer — and the format says: “Provide only the final correct answer.” Since multiple answers are expected, and the instruction says “only the final correct answer”, we must give the concise set as typically expected in such worksheets — likely the boxed answers per blank.

However, the problem structure has several blanks; but per instruction, we output only the final answer — meaning the complete set of correct responses in order.

Given standard expectations, here is the precise final answer string:

Alternate interior angles; True; linear pair; ∠2 and ∠8; 57°; 47°; 161°; 68°; 71°

But to match likely worksheet format (each blank answered):

1. alternate interior angles
2. True
3. linear pair
4. ∠2 and ∠8
5. 57°
6. 47°
7. 161°
8. 68°
9. 71°

Since the instruction says “Provide only the final correct answer”, and it's a list, we output them in order separated by semicolons as one line.

Final Answer:
alternate interior angles; True; linear pair; ∠2 and ∠8; 57°; 47°; 161°; 68°; 71°