Using facts the angles formed when paralle lines are cut by a transversel waht relationship can you establish between angle 5 and 1?

When parallel lines are cut by a transversal, the following relationships between the angles are established:

1. **Corresponding Angles**: Angles that are in the same position relative to the parallel lines and the transversal. They are equal.
2. **Alternate Interior Angles**: Angles that are on opposite sides of the transversal and inside the parallel lines. They are equal.
3. **Alternate Exterior Angles**: Angles that are on opposite sides of the transversal and outside the parallel lines. They are equal.
4. **Vertical Angles**: Angles that are opposite each other when two lines intersect. They are equal.

Without a specific diagram, it's difficult to identify the exact angles labeled as 5 and 1. However, typically in the context of parallel lines cut by a transversal:

- If Angle 5 is in the same position (for example, both are in the top-right corner relative to the transversal and parallel lines), they are **corresponding angles** and equal.
- If Angle 5 is on the opposite side and inside the parallel lines compared to Angle 1, they are **alternate interior angles** and equal.
- If Angle 5 is on the opposite side and outside the parallel lines compared to Angle 1, they are **alternate exterior angles** and equal.
- If Angle 5 and Angle 1 are directly opposite each other at the point where the lines intersect, they are **vertical angles** and also equal.

To determine the correct relationship between Angle 5 and Angle 1, please refer to the positions of these angles in the figure. If you provide a diagram or description of their locations, I can help confirm the relationship!

a 2 is infront of 1 then after 2 is 5

Based on your description, it seems you are referencing a situation where angle 2 is adjacent to angle 1, and angle 5 is adjacent to angle 2. This is typically how these angles are positioned when parallel lines are cut by a transversal.

Here's a possible configuration:

```
Parallel Line 1
1
|
---- Transversal -----
2 | 5
----
Parallel Line 2
```

In this arrangement:

- Angle 1 and Angle 2 are adjacent angles.
- Angle 2 is likely an interior angle, while Angle 5 could be either an interior or exterior angle depending on the exact positioning in relation to the transversal.

### Relationship between Angle 5 and Angle 1

Given the way you described the angles:
- If Angle 2 and Angle 5 are vertically opposite, then Angle 5 equals Angle 2.
- However, typically, when discussing parallel lines and non-adjacent angles in a transversal context, we consider corresponding angles, alternate interior angles, etc.

### Correct Relationship
If angle 1 is on the same side of the transversal as angle 2 and both angles are on the interior of the two parallel lines (making Angle 5 an alternate interior angle relative to Angle 1), then you can conclude that:

- **Angle 1 and Angle 5 are alternate interior angles** and therefore **equal** if lines are parallel.

### Conclusion
Based on how you described the configuration, it could imply Angle 5 and Angle 1 are alternate interior angles. Thus, if lines are indeed parallel and the angles are positioned as you've explained, they would be equal.

If you can verify the specific positions in a diagram, that will confirm this relationship!