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.
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1)
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Given: One angle = 68°, find x°
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Type of angle pair: Corresponding
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Relationship: Congruent (corresponding angles are equal when lines are parallel)
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So: x = 68°
✔
✔ Correct.
> *Explanation:* Corresponding angles are in matching corners and are congruent when the lines are parallel.
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2)
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Given: One angle = 134°, find x°
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Type of angle pair: Same-Side Interior
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Relationship: Supplementary (same-side interior angles add up to 180°)
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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°).
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3)
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Given: One angle = 120°, find x°
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Type of angle pair: Vertical
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Relationship: Congruent (vertical angles are always equal)
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So: x = 120°
✔
✔ Correct.
> *Explanation:* Vertical angles are opposite angles formed by two intersecting lines; they are always congruent.
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4)
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Given: One angle = 101°, find x°
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Type of angle pair: Alternate Interior
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Relationship: Congruent (alternate interior angles are equal when lines are parallel)
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So: x = 101°
✔
✔ Correct.
> *Explanation:* Alternate interior angles are on opposite sides of the transversal and inside the parallel lines. They are congruent.
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5)
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Given: One angle = 77°, find x°
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Type of angle pair: Same-Side Exterior
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Relationship: Supplementary (same-side exterior angles add to 180°)
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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.
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6)
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Given: One angle = 106°, find x°
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Type of angle pair: Alternate Interior
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Relationship: Congruent
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So: x = 106°
✔
✔ Correct.
> *Explanation:* Again, alternate interior angles are congruent when lines are parallel.
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7)
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Given: One angle = 74°, find x°
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Type of angle pair: Same-Side Interior
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Relationship: Supplementary
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So: x = 180° – 74° = 106°
✔
✔ Correct.
> *Explanation:* These are interior angles on the same side of the transversal — they add to 180°.
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8)
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Given: One angle = 142°, find x°
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Type of angle pair: Alternate Exterior
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Relationship: Congruent (alternate exterior angles are equal)
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So: x = 142°
✔
✔ Correct.
> *Explanation:* Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines. They are congruent.
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✔ Summary: All answers on the worksheet are correct!
Here’s a quick recap of the
angle pair types and their properties:
| 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 (sum to 180°) |
|
Same-Side Exterior | Same side, outside | Supplementary (sum to 180°) |
|
Vertical | Opposite angles at intersection | Congruent |
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Final Answer:
All solutions provided in the worksheet are
correct, with proper identification of angle pairs and accurate calculations.
✔ All answers are correct!
Parent Tip: Review the logic above to help your child master the concept of angle relationships worksheet answers.
