Geometry worksheet displaying eight problems where students identify angle pairs formed by parallel lines cut by a transversal and solve for x.

The image you've uploaded is a worksheet titled "Angle Pairs Created by Parallel Lines Cut by a Transversal." The task is to:

- Identify the type of angle pair formed when two parallel lines are cut by a transversal.
- Determine whether the angles are congruent or supplementary.
- Use that relationship to find the missing angle measurement (x°).

Let’s go through each problem step-by-step and verify the solutions.

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🔷 Problem 1:

- Given: One angle = 68°, x° is the corresponding angle.
- Type of angle pair: Corresponding
- Relationship: Congruent (corresponding angles are equal when lines are parallel)
- So: $ x = 68^\circ $

✔ Correct.

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🔷 Problem 2:

- Given: One angle = 134°, x° is on the same side inside the parallel lines.
- Type of angle pair: Same-Side Interior
- Relationship: Supplementary (same-side interior angles add up to 180°)
- So: $ x = 180^\circ - 134^\circ = 46^\circ $

✔ Correct.

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🔷 Problem 3:

- Given: One angle = 120°, x° is vertically opposite to it.
- Type of angle pair: Vertical
- Relationship: Congruent (vertical angles are always equal)
- So: $ x = 120^\circ $

✔ Correct.

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🔷 Problem 4:

- Given: One angle = 101°, x° is alternate interior.
- Type of angle pair: Alternate Interior
- Relationship: Congruent (alternate interior angles are equal when lines are parallel)
- So: $ x = 101^\circ $

✔ Correct.

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🔷 Problem 5:

- Given: One angle = 77°, x° is on the same side outside the parallel lines.
- Type of angle pair: Same-Side Exterior
- Relationship: Supplementary (same-side exterior angles add to 180°)
- So: $ x = 180^\circ - 77^\circ = 103^\circ $

✔ Correct.

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🔷 Problem 6:

- Given: One angle = 106°, x° is alternate interior.
- Type of angle pair: Alternate Interior
- Relationship: Congruent
- So: $ x = 106^\circ $

✔ Correct.

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🔷 Problem 7:

- Given: One angle = 74°, x° is on the same side inside the lines.
- Type of angle pair: Same-Side Interior
- Relationship: Supplementary
- So: $ x = 180^\circ - 74^\circ = 106^\circ $

✔ Correct.

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🔷 Problem 8:

- Given: One angle = 142°, x° is alternate exterior.
- Type of angle pair: Alternate Exterior
- Relationship: Congruent (alternate exterior angles are equal)
- So: $ x = 142^\circ $

✔ Correct.

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✔ Summary:

All answers in the worksheet are correctly filled out.

Here's a quick reference table:

| Problem | Angle Pair Type | Relationship | x° Value |
|--------|-------------------------|------------------|----------|
| 1 | Corresponding | Congruent | 68° |
| 2 | Same-Side Interior | Supplementary | 46° |
| 3 | Vertical | Congruent | 120° |
| 4 | Alternate Interior | Congruent | 101° |
| 5 | Same-Side Exterior | Supplementary | 103° |
| 6 | Alternate Interior | Congruent | 106° |
| 7 | Same-Side Interior | Supplementary | 106° |
| 8 | Alternate Exterior | Congruent | 142° |

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📌 Key Concepts Used:

- Corresponding Angles: Equal → congruent
- Alternate Interior/Exterior: Equal → congruent
- Same-Side Interior/Exterior: Add to 180° → supplementary
- Vertical Angles: Always equal

These relationships only apply when the two lines are parallel, which is assumed here.

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✔ Final Answer: All solutions are correct as shown in the worksheet.