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In the given diagram, lines \( r \) and \( g \) are parallel, and \( t \) is the transversal intersecting them. The question asks why \(\angle 5\) and \(\angle 8\) are congruent.

From the figure:

- \(\angle 5\) is on the upper left side of the transversal \( t \) on line \( r \).
- \(\angle 8\) is on the lower right side of the transversal \( t \) on line \( g \).

\(\angle 5\) and \(\angle 8\) are positioned on opposite sides of the transversal and on the outside of the parallel lines \( r \) and \( g \). This means they are **Alternate Exterior Angles**, which are always congruent when the lines are parallel.

Thus, the correct answer is:

**Alternate exterior angles**

Would you like more details or have any other questions?

Here are 5 related questions:
1. What are alternate interior angles, and how are they different from alternate exterior angles?
2. How can you prove that alternate exterior angles are congruent?
3. What happens to alternate exterior angles if the lines are not parallel?
4. How can you identify other pairs of alternate exterior angles in a diagram?
5. How do corresponding angles differ from alternate exterior angles?

**Tip**: Remember, alternate exterior angles are always congruent when two parallel lines are cut by a transversal.

∠5 and ∠8 are congruent because they are ___________________.

Understand why ∠5 and ∠8 are congruent in this geometry problem. Explore the relationship between parallel lines, transversals, and alternate exterior angles. This explanation is suitable for students in Grades 7-9 learning about angle theorems.

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