The problem asks which of the following statements is false, given the diagram of two parallel lines intersected by a transversal. Here's the breakdown:

1. $\angle 1 = \angle 5$:

   • $\angle 1$ and $\angle 5$ are corresponding angles because they are on the same side of the transversal and in the same relative position at each intersection. Corresponding angles are equal when the lines are parallel, so this statement is true.

2. \angle 3 + \(\angle 5 = 180^\circ:

   • $\angle 3$ and $\angle 5$ are consecutive interior angles (same side of the transversal). For parallel lines, consecutive interior angles add up to $180^\circ$, so this statement is true.

3. \angle 6 = \(\angle 8:

   • $\angle 6$ and $\angle 8$ are vertically opposite angles, and vertically opposite angles are always equal. Thus, this statement is true.

4. \angle 3 = \(\angle 7:

   • $\angle 3$ and $\angle 7$ are alternate interior angles (they lie on opposite sides of the transversal). For parallel lines, alternate interior angles are equal. Therefore, this statement is true.

Since all of the statements appear to be true, none of them are false. However, there might be a typographical error in the provided options. Could you please double-check the image for any details I might have missed?

Let me know if you need further clarifications or have any additional questions!

Questions for deeper understanding:

1. What are corresponding angles, and how can you identify them?
2. How do you determine if two angles are alternate interior angles?
3. What is the relationship between vertically opposite angles?
4. Can you explain why consecutive interior angles sum up to $180^\circ$?
5. What would happen to these angle relationships if the lines were not parallel?

Tip: When working with angles formed by a transversal intersecting parallel lines, remember that corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to $180^\circ$).