https://file.aiquickdraw.com/mathbot/file/1726532554191vx2uw5dg.jpg

In this image, we are asked to identify which angles are congruent to each other. The diagram depicts two intersecting lines crossed by a transversal, forming several pairs of angles.

### Types of congruent angles when two lines are intersected by a transversal:
1. **Corresponding Angles**: These are angles that are in the same position on the two intersecting lines. They are congruent.
2. **Alternate Interior Angles**: These angles are on opposite sides of the transversal and inside the two lines. They are congruent.
3. **Alternate Exterior Angles**: These angles are on opposite sides of the transversal and outside the two lines. They are congruent.
4. **Vertically Opposite Angles**: Angles that are opposite each other when two lines intersect. They are congruent.

Let's analyze the provided angles:

1. **Angles 7 and 1** are **alternate exterior angles**, so they are congruent.
2. **Angles 5 and 7** do not follow any of the rules for congruence.
3. **Angles 3 and 8** are not congruent by any rule.
4. **Angles 8 and 7** are **vertically opposite angles**, and they are congruent.

Thus, the correct answer is **"∠8 and ∠7"**.

Would you like a more detailed explanation of any of these congruence rules or the specific types of angles in the image?

### Related Questions:
1. What are corresponding angles in this diagram?
2. Can you explain why alternate interior angles are congruent?
3. What is the difference between alternate exterior and alternate interior angles?
4. How do vertically opposite angles occur in intersecting lines?
5. Why aren't angles 3 and 8 congruent in this diagram?

**Tip**: Remember that alternate interior, alternate exterior, and corresponding angles are congruent only when the lines are parallel.

Which angles are congruent to each other?

Learn how to identify congruent angles when two lines are intersected by a transversal. This problem covers concepts like alternate exterior angles and vertically opposite angles, suitable for students in Grades 7-9.

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