Educational chart explaining angle pairs formed when a transversal intersects parallel lines, with definitions and diagrams.

It looks like you've uploaded an educational worksheet titled "Angle Pairs Created by Parallel Lines Cut by a Transversal." This is a reference guide explaining the different types of angle pairs formed when a transversal intersects two parallel lines. There isn't a specific problem to solve here — instead, this is a vocabulary and concept summary.

However, I can help explain the key concepts and how to use this information to solve related geometry problems.

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🔍 Explanation of the Concepts

Let’s break down each term and what it means:

#### 1. Transversal
- A line that crosses two or more parallel lines.
- It creates eight angles at the points of intersection.
- These angles form special relationships based on their positions.

#### 2. Congruent Angles
- Angles that have the same measure (equal in degrees).
- Marked with the same number of arcs in diagrams.

#### 3. Supplementary Angles
- Two angles that add up to 180°.
- They are often adjacent (next to each other) or on the same side of the transversal.

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📐 Angle Pairs When Parallel Lines Are Cut by a Transversal

Here are the five main types of angle pairs:

| Type | Definition | Relationship |
|------|-----------|--------------|
| Corresponding Angles | Same side of the transversal and same side of the parallel lines (like "F" shape). | ✔ Congruent |
| Alternate Interior Angles | Opposite sides of the transversal, inside the parallel lines ("Z" shape). | ✔ Congruent |
| Alternate Exterior Angles | Opposite sides of the transversal, outside the parallel lines. | ✔ Congruent |
| Same-Side Interior Angles | Same side of the transversal, inside the lines ("U" shape). | ✘ Supplementary (add to 180°) |
| Same-Side Exterior Angles | Same side of the transversal, outside the lines. | ✘ Supplementary (add to 180°) |
| Vertical Angles | Angles opposite each other where lines cross. | ✔ Congruent |

> ⚠️ Note: Vertical angles are formed anytime two lines intersect — not just with parallel lines.

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✔ Example Problem (Based on This Concept)

Problem:
Two parallel lines are cut by a transversal. One angle measures 65°. Find the measure of its:
- Corresponding angle
- Alternate interior angle
- Same-side interior angle

Solution:
- Corresponding angle: Same as original → 65° (congruent)
- Alternate interior angle: Also congruent → 65°
- Same-side interior angle: Supplementary → 180° – 65° = 115°

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💡 Tips for Solving Problems Like This:

1. Label the angles if given a diagram.
2. Use the angle pair names to determine if angles are equal or add to 180°.
3. Remember: Only corresponding, alternate interior, alternate exterior, and vertical angles are congruent.
4. Same-side interior and exterior angles are supplementary.
5. Vertical angles are always congruent, regardless of whether lines are parallel.

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🧩 Summary

This sheet is a great reference tool for solving problems involving:
- Finding missing angle measures
- Proving lines are parallel
- Using angle relationships in proofs

If you have a specific problem (like a diagram with labeled angles), feel free to describe it or upload it, and I’ll walk you through solving it step-by-step using these rules!

Let me know how I can help further! 😊