Angle Pairs Created By Parallel Lines Cut By A Transversal - Fill ... - Free Printable

Let's solve each of the 8 problems step by step, identifying the type of angle pair formed when two parallel lines are cut by a transversal, and then determining whether the angles are congruent or supplementary, and finally finding the missing measurement.

We'll use these key concepts:

- Corresponding angles: Equal (congruent) — same position at each intersection.
- Alternate interior angles: Equal (congruent) — on opposite sides of the transversal, inside the parallel lines.
- Alternate exterior angles: Equal (congruent) — on opposite sides of the transversal, outside the parallel lines.
- Same-side interior angles: Supplementary (add to 180°) — on the same side of the transversal, inside the lines.
- Same-side exterior angles: Supplementary (add to 180°) — on the same side of the transversal, outside the lines.

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1)

- Given: One angle is 68°
- Angle pair type: Corresponding
- These angles are: Congruent
- So, the missing angle = 68°

✔ Answer: 68°

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2)

- Given: One angle is 134°
- Angle pair type: Same-side Interior
- These angles are: Supplementary
- So, missing angle = 180° − 134° = 46°

✔ Answer: 46°

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3)

- Given: One angle is 100°
- Angle pair type: Vertical angles → but the problem says "Type of angle pair" based on the transversal. Wait — this looks like Alternate Interior? Let's analyze.

Wait — actually, looking at the diagram:
- The angle marked 100° and the one we're solving for are on opposite sides of the transversal and inside the parallel lines → that’s Alternate Interior Angles.
- Alternate Interior Angles are Congruent.

So:
- Type: Alternate Interior
- These angles are: Congruent
- So, missing angle = 100°

✔ Answer: 100°

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4)

- Given: One angle is 111°
- Angle pair type: Alternate Exterior
- These angles are: Congruent
- So, missing angle = 111°

✔ Answer: 111°

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5)

- Given: One angle is 72°
- Angle pair type: Same-side Interior
- These angles are: Supplementary
- So, missing angle = 180° − 72° = 108°

✔ Answer: 108°

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6)

- Given: One angle is 106°
- Angle pair type: Alternate Interior
- These angles are: Congruent
- So, missing angle = 106°

✔ Answer: 106°

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7)

- Given: One angle is 74°
- Angle pair type: Same-side Interior
- These angles are: Supplementary
- So, missing angle = 180° − 74° = 106°

✔ Answer: 106°

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8)

- Given: One angle is 145°
- Angle pair type: Alternate Exterior
- These angles are: Congruent
- So, missing angle = 145°

✔ Answer: 145°

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✔ Final Answers:

| Problem | Angle Pair Type | Relationship | Missing Angle |
|--------|------------------------|------------------|---------------|
| 1 | Corresponding | Congruent | 68° |
| 2 | Same-side Interior | Supplementary | 46° |
| 3 | Alternate Interior | Congruent | 100° |
| 4 | Alternate Exterior | Congruent | 111° |
| 5 | Same-side Interior | Supplementary | 108° |
| 6 | Alternate Interior | Congruent | 106° |
| 7 | Same-side Interior | Supplementary | 106° |
| 8 | Alternate Exterior | Congruent | 145° |

> Note: In problem #3, the image shows a 100° angle and an unknown angle across from it on the opposite side of the transversal and between the lines — so Alternate Interior is correct.

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