We are given a series of intersecting lines, and we need to determine which lines are parallel based on the provided angle relationships.

Key information:

• At the intersection of lines $a$ and $e$, there is a right angle of 110° (possibly referring to an exterior angle or angle adjacent to a right angle).
• At the intersection of lines $b$ and $e$, there is a right angle of 110° (similarly, likely referring to an exterior angle).
• At the intersection of lines $b$ and $f$, the bottom right angle is 80°.

Solution process:

We can apply geometric principles such as corresponding angles, supplementary angles, and congruent angles to check for parallelism.

1. Lines a and b being parallel:

   • To check if lines $a$ and $b$ are parallel, we can use the corresponding angles theorem, which states that if two lines are cut by a transversal, and corresponding angles are congruent, then the lines are parallel.
   • From the problem, we are told that the angle at the intersection of line $a$ and line $e$ is congruent to the angle at the intersection of line $b$ and line $e$ (both are 110°). Since these are corresponding angles, lines $a$ and $b$ are parallel.

2. Lines e and f being parallel:

   • To check if lines $e$ and $f$ are parallel, we need to look at the relationship between the angles formed by their intersection with line $b$.
   • We are told that at the intersection of lines $b$ and $f$, the bottom right angle is 80°. By the same side exterior angle theorem, if the same-side exterior angles (110° and 80°) are supplementary, then the lines $e$ and $f$ are parallel.

Conclusion:

• Lines a and b are parallel because their corresponding angles are congruent (both 110°).
• Lines e and f are parallel because their same side exterior angles are supplementary (110° and 80°).

Answer justification:

The correct statements are:

• Lines a and b are parallel because their corresponding angles are congruent.
• Lines e and f are parallel because their same side exterior angles are supplementary.

Would you like further clarification on any step? Or do you have other questions?

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Additional Related Questions:

1. What is the converse of the corresponding angles postulate?
2. How do supplementary angles relate to parallel lines?
3. Can two lines intersect at more than one point in Euclidean geometry?
4. How can we use vertical angles to prove lines are parallel?
5. What are alternate interior angles, and how do they help in proving parallelism?

Tip: When looking for parallel lines in geometry, always check for corresponding, alternate interior, or same-side exterior angles!