Practice worksheet for identifying angle pairs formed by parallel lines and a transversal, including corresponding, alternate interior, same-side interior, and vertical angles.
Worksheet titled "Angle Pairs Created by Parallel Lines Cut by a Transversal" with eight problems showing angle pairs, their types, and missing angle measurements.
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Step-by-step solution for: Angle Pairs Created By Parallel Lines Cut By A Transversal - Fill ...
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Step-by-step solution for: Angle Pairs Created By Parallel Lines Cut By A Transversal - Fill ...
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 one by one, verify the answers, and explain the reasoning.
---
- Given: One angle = 68°, find x°
- Type of angle pair: Corresponding
- Relationship: Congruent (corresponding angles are equal when lines are parallel)
- So: x = 68° ✔
✔ Correct.
> *Explanation:* Corresponding angles are in matching corners and are congruent when the lines are parallel.
---
- Given: One angle = 134°, find x°
- Type of angle pair: Same-Side Interior
- Relationship: Supplementary (same-side interior angles add up to 180°)
- So: x = 180° – 134° = 46° ✔
✔ Correct.
> *Explanation:* Same-side interior angles are on the same side of the transversal and inside the parallel lines. They are supplementary (add to 180°).
---
- Given: One angle = 120°, find x°
- Type of angle pair: Vertical
- Relationship: Congruent (vertical angles are always equal)
- So: x = 120° ✔
✔ Correct.
> *Explanation:* Vertical angles are opposite angles formed by two intersecting lines; they are always congruent.
---
- Given: One angle = 101°, find x°
- Type of angle pair: Alternate Interior
- Relationship: Congruent (alternate interior angles are equal when lines are parallel)
- So: x = 101° ✔
✔ Correct.
> *Explanation:* Alternate interior angles are on opposite sides of the transversal and inside the parallel lines. They are congruent.
---
- Given: One angle = 77°, find x°
- Type of angle pair: Same-Side Exterior
- Relationship: Supplementary (same-side exterior angles add to 180°)
- So: x = 180° – 77° = 103° ✔
✔ Correct.
> *Explanation:* Same-side exterior angles are on the same side of the transversal and outside the parallel lines. They are supplementary.
---
- Given: One angle = 106°, find x°
- Type of angle pair: Alternate Interior
- Relationship: Congruent
- So: x = 106° ✔
✔ Correct.
> *Explanation:* Again, alternate interior angles are congruent when lines are parallel.
---
- Given: One angle = 74°, find x°
- Type of angle pair: Same-Side Interior
- Relationship: Supplementary
- So: x = 180° – 74° = 106° ✔
✔ Correct.
> *Explanation:* These are interior angles on the same side of the transversal → supplementary.
---
- Given: One angle = 142°, find x°
- Type of angle pair: Alternate Exterior
- Relationship: Congruent
- So: x = 142° ✔
✔ Correct.
> *Explanation:* Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines. They are congruent.
---
| Problem | Angle Pair Type | Relationship | x° |
|--------|-------------------------|--------------------|------|
| 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° |
All answers on the worksheet are correctly filled in.
---
When parallel lines are cut by a transversal, the following angle pairs are formed:
| Angle Pair Type | Location | Relationship |
|-------------------------|------------------------------|------------------|
| Corresponding | Same relative position | Congruent |
| Alternate Interior | Opposite sides, inside | Congruent |
| Alternate Exterior | Opposite sides, outside | Congruent |
| Same-Side Interior | Same side, inside | Supplementary |
| Same-Side Exterior | Same side, outside | Supplementary |
| Vertical | Opposite angles at an intersection | Congruent |
---
✔ Final Answer: All answers on the worksheet are correct.
Each angle pair type was properly identified, and the missing measurements were calculated accurately using the appropriate geometric relationships.
- 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 one by one, verify the answers, and explain the reasoning.
---
1)
- Given: One angle = 68°, find x°
- Type of angle pair: Corresponding
- Relationship: Congruent (corresponding angles are equal when lines are parallel)
- So: x = 68° ✔
✔ Correct.
> *Explanation:* Corresponding angles are in matching corners and are congruent when the lines are parallel.
---
2)
- Given: One angle = 134°, find x°
- Type of angle pair: Same-Side Interior
- Relationship: Supplementary (same-side interior angles add up to 180°)
- So: x = 180° – 134° = 46° ✔
✔ Correct.
> *Explanation:* Same-side interior angles are on the same side of the transversal and inside the parallel lines. They are supplementary (add to 180°).
---
3)
- Given: One angle = 120°, find x°
- Type of angle pair: Vertical
- Relationship: Congruent (vertical angles are always equal)
- So: x = 120° ✔
✔ Correct.
> *Explanation:* Vertical angles are opposite angles formed by two intersecting lines; they are always congruent.
---
4)
- Given: One angle = 101°, find x°
- Type of angle pair: Alternate Interior
- Relationship: Congruent (alternate interior angles are equal when lines are parallel)
- So: x = 101° ✔
✔ Correct.
> *Explanation:* Alternate interior angles are on opposite sides of the transversal and inside the parallel lines. They are congruent.
---
5)
- Given: One angle = 77°, find x°
- Type of angle pair: Same-Side Exterior
- Relationship: Supplementary (same-side exterior angles add to 180°)
- So: x = 180° – 77° = 103° ✔
✔ Correct.
> *Explanation:* Same-side exterior angles are on the same side of the transversal and outside the parallel lines. They are supplementary.
---
6)
- Given: One angle = 106°, find x°
- Type of angle pair: Alternate Interior
- Relationship: Congruent
- So: x = 106° ✔
✔ Correct.
> *Explanation:* Again, alternate interior angles are congruent when lines are parallel.
---
7)
- Given: One angle = 74°, find x°
- Type of angle pair: Same-Side Interior
- Relationship: Supplementary
- So: x = 180° – 74° = 106° ✔
✔ Correct.
> *Explanation:* These are interior angles on the same side of the transversal → supplementary.
---
8)
- Given: One angle = 142°, find x°
- Type of angle pair: Alternate Exterior
- Relationship: Congruent
- So: x = 142° ✔
✔ Correct.
> *Explanation:* Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines. They are congruent.
---
✔ Summary of All Answers:
| Problem | Angle Pair Type | Relationship | x° |
|--------|-------------------------|--------------------|------|
| 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° |
All answers on the worksheet are correctly filled in.
---
🔍 Key Concepts Recap:
When parallel lines are cut by a transversal, the following angle pairs are formed:
| Angle Pair Type | Location | Relationship |
|-------------------------|------------------------------|------------------|
| Corresponding | Same relative position | Congruent |
| Alternate Interior | Opposite sides, inside | Congruent |
| Alternate Exterior | Opposite sides, outside | Congruent |
| Same-Side Interior | Same side, inside | Supplementary |
| Same-Side Exterior | Same side, outside | Supplementary |
| Vertical | Opposite angles at an intersection | Congruent |
---
✔ Final Answer: All answers on the worksheet are correct.
Each angle pair type was properly identified, and the missing measurements were calculated accurately using the appropriate geometric relationships.
Parent Tip: Review the logic above to help your child master the concept of angle relationships and parallel lines worksheet.
