The question in your image asks which condition is sufficient to show that lines $n$ and $p$ are parallel. From the diagram and the answer options, this is a problem about the properties of angles formed by transversals and parallel lines.

Key Concepts:

• Corresponding Angles Postulate: If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
• Alternate Interior Angles Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.
• Consecutive Interior Angles: If two lines are cut by a transversal and the consecutive interior angles are supplementary, the lines are parallel.

Answer:

From the options:

• Option C: $\angle 2 \cong \angle 7$ is correct.

These are corresponding angles, and by the Corresponding Angles Postulate, if these angles are congruent, it proves that lines $n$ and $p$ are parallel.

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Related Questions:

1. What are alternate interior angles, and how do they help in proving parallel lines?
2. How does the corresponding angles postulate work in geometry?
3. Can consecutive interior angles also prove lines parallel?
4. What happens if two lines are perpendicular instead of parallel in similar angle conditions?
5. How can we determine parallelism using angle pairs formed by more than one transversal?

Tip: Whenever two lines are cut by a transversal, always check for pairs of corresponding or alternate interior angles to prove parallelism.