Angles and Parallel Lines Worksheets :: 49 - 72 - Free Printable

It looks like you've uploaded an image containing a worksheet titled "Geometry 1-3: Parallel Lines" with several problems related to parallel lines, transversals, and angle relationships. Since I can't view images directly, I’ll help you solve the problems based on the text you provided (which appears to be from the worksheet). Let's go through each section step by step.

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🔷 Problem Set 1: Given: \( m\angle 1 = 78^\circ \)

We are given that \( m\angle 1 = 78^\circ \), and we need to find other angles using properties of parallel lines and transversals.

Assuming this is a standard diagram with two parallel lines cut by a transversal, here are common angle relationships:

- Corresponding angles are equal.
- Alternate interior angles are equal.
- Same-side interior angles are supplementary (add to 180°).
- Vertical angles are equal.
- Linear pairs add to 180°.

Let’s suppose the diagram has labeled angles around a transversal intersecting two parallel lines.

#### Given: \( m\angle 1 = 78^\circ \)

1. \( m\angle 2 = ? \)
If ∠1 and ∠2 are vertical angles → then \( m\angle 2 = 78^\circ \)
If they are linear pair → \( m\angle 2 = 180^\circ - 78^\circ = 102^\circ \)

But since it says "Given: \( m\angle 1 = 78^\circ \)", and asks for \( m\angle 2 \), likely ∠1 and ∠2 are adjacent or vertical.

Without the exact diagram, assume:
- ∠1 and ∠2 are vertical angles → \( m\angle 2 = 78^\circ \)
- Or ∠1 and ∠2 are linear pair → \( m\angle 2 = 102^\circ \)

But let's look at typical labeling: often ∠1 and ∠2 are adjacent on a straight line.

Wait — in many textbooks, ∠1 and ∠2 are adjacent angles forming a linear pair if they are next to each other on a line.

So if ∠1 and ∠2 are supplementary, then:
> \( m\angle 2 = 180^\circ - 78^\circ = 102^\circ \)

✔ Answer: 102°

2. \( m\angle 3 = ? \)
If ∠3 is corresponding or alternate interior to ∠1, and lines are parallel, then \( m\angle 3 = 78^\circ \)

Likely ∠3 is corresponding to ∠1 → \( m\angle 3 = 78^\circ \)

✔ Answer: 78°

3. \( m\angle 4 = ? \)
If ∠4 is same-side interior to ∠1, then they are supplementary → \( m\angle 4 = 102^\circ \)

Or if ∠4 is vertical to ∠2 → same as ∠2

But again, assuming standard labeling:

If ∠1 and ∠4 are vertical angles, then ∠4 = 78°
But if ∠1 and ∠4 are on opposite sides of the transversal, maybe alternate exterior?

Let's assume the standard diagram where:

- ∠1 and ∠5 are vertical
- ∠1 and ∠3 are corresponding
- ∠1 and ∠4 are same-side interior → supplementary

So if ∠4 is on the same side, then:
> \( m\angle 4 = 180^\circ - 78^\circ = 102^\circ \)

✔ Answer: 102°

4. \( m\angle 5 = ? \)
If ∠5 is vertical to ∠1 → \( m\angle 5 = 78^\circ \)

✔ Answer: 78°

So far:

| Question | Answer |
|--------|--------|
| 1. \( m\angle 2 \) | 102° |
| 2. \( m\angle 3 \) | 78° |
| 3. \( m\angle 4 \) | 102° |
| 4. \( m\angle 5 \) | 78° |

> ✔ These are typical values based on parallel lines and transversals.

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🔷 Problem Set 2: Given: \( m\angle 6 = 48^\circ \)

Now given: \( m\angle 6 = 48^\circ \)

Again, assuming same setup.

5. \( m\angle 7 = ? \)
If ∠6 and ∠7 are vertical → same measure → \( m\angle 7 = 48^\circ \)

✔ Answer: 48°

6. \( m\angle 8 = ? \)
If ∠8 is linear pair with ∠6 → \( m\angle 8 = 180^\circ - 48^\circ = 132^\circ \)

✔ Answer: 132°

7. \( m\angle 9 = ? \)
If ∠9 is corresponding to ∠6 → \( m\angle 9 = 48^\circ \)

✔ Answer: 48°

8. \( m\angle 10 = ? \)
If ∠10 is same-side interior with ∠6 → supplementary → \( m\angle 10 = 132^\circ \)

✔ Answer: 132°

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🔷 Problem Set 3: Given: \( m\angle A = 120^\circ \), \( m\angle B = 60^\circ \)

This might be about determining whether lines are parallel.

But since no diagram, assume:

- Two lines cut by a transversal
- \( m\angle A = 120^\circ \), \( m\angle B = 60^\circ \)

Check if they are supplementary? Yes, 120 + 60 = 180° → could be same-side interior angles.

If they are same-side interior angles and sum to 180°, then the lines are parallel.

So question likely is: Are the lines parallel?

→ Yes, because same-side interior angles are supplementary.

✔ Answer: Yes, the lines are parallel.

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🔷 Problem Set 4: Use the diagram to answer the questions

You mentioned there's a diagram with points labeled A, B, C, D, etc., but without seeing it, I can only guess.

But looking at your text:

> "Use the diagram to answer the following questions."

And below, there are blanks.

Possibly asking for:

- Which lines are parallel?
- Which angles are congruent?
- Find missing angle measures?

Since no specific questions are typed out, I'll assume common ones.

For example:

Question: Name a pair of corresponding angles.

→ ∠1 and ∠5

Question: Name a pair of alternate interior angles.

→ ∠3 and ∠6

Question: Name a pair of same-side interior angles.

→ ∠3 and ∠5

Question: If \( m\angle 1 = 110^\circ \), find \( m\angle 4 \)

→ If ∠1 and ∠4 are same-side interior → \( m\angle 4 = 70^\circ \)

But without exact questions, I can’t give precise answers.

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🔷 Final Notes

To summarize, here are the most likely answers based on standard geometry problems involving parallel lines:

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✔ Solutions (Based on Standard Diagrams):

#### Set 1: \( m\angle 1 = 78^\circ \)

1. \( m\angle 2 = 102^\circ \) (linear pair)
2. \( m\angle 3 = 78^\circ \) (corresponding)
3. \( m\angle 4 = 102^\circ \) (same-side interior)
4. \( m\angle 5 = 78^\circ \) (vertical)

#### Set 2: \( m\angle 6 = 48^\circ \)

5. \( m\angle 7 = 48^\circ \) (vertical)
6. \( m\angle 8 = 132^\circ \) (linear pair)
7. \( m\angle 9 = 48^\circ \) (corresponding)
8. \( m\angle 10 = 132^\circ \) (same-side interior)

#### Set 3: \( m\angle A = 120^\circ \), \( m\angle B = 60^\circ \)

9. Are the lines parallel? → Yes, because same-side interior angles are supplementary.

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📌 Key Concepts Used:

- Vertical angles: Equal
- Linear pairs: Add to 180°
- Corresponding angles: Equal if lines are parallel
- Alternate interior angles: Equal if lines are parallel
- Same-side interior angles: Supplementary if lines are parallel

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If you can describe the diagram or provide the actual questions (e.g., “Find \( m\angle 3 \)” or “Are lines l and m parallel?”), I can give even more precise answers.

Let me know!