https://file.aiquickdraw.com/mathbot/file/172771234482194gsbg5k.jpg

In this image, we are tasked with identifying which angles are congruent to each other based on the given diagram.

To solve this, we analyze the arrangement of the lines and angles in the diagram:

- The diagram appears to show two intersecting lines, with angles labeled around the intersection points.
- When two lines intersect, they form pairs of **vertical angles**, which are always congruent.

Let's identify the vertical angles:
1. ∠2 and ∠7 are **vertical angles**, so they are congruent.
2. ∠5 and ∠4 are **not** vertical angles, so they are not congruent.
3. ∠7 and ∠4 are **not** vertical angles, so they are not congruent.
4. ∠2 and ∠4 are **not** vertical angles, so they are not congruent.

Thus, the correct answer is **∠2 and ∠7**.

Would you like further clarification or details on this problem? Here are five related questions to help deepen your understanding:

1. What are alternate interior angles, and how do they relate to congruent angles?
2. How do corresponding angles form, and when are they congruent?
3. Can vertical angles ever be non-congruent?
4. How can supplementary angles be identified in this diagram?
5. What are some other properties of intersecting lines that apply to angle relationships?

**Tip:** When identifying congruent angles, always look for vertical, alternate interior, and corresponding angle pairs!

Which angles are congruent to each other?

Learn how to identify congruent angles in a diagram with intersecting lines. This problem covers key geometric concepts, including vertical angles and congruence. Suitable for students in Grades 6-8.

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