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The question asks whether each pair of remote interior angles in a triangle has two exterior angles. The problem is clarified through the diagram choices, which relate to the concept of **remote interior angles** and **exterior angles** in triangles.

Here's a breakdown of the relevant geometric concepts:
- **Exterior angles** of a triangle are formed when one side of a triangle is extended outward. The angle formed between this extended side and the adjacent side is called the exterior angle.
- The **remote interior angles** of a triangle are the two non-adjacent interior angles to a given exterior angle. For example, if the exterior angle is at one vertex, the remote interior angles are at the other two vertices.

Let's evaluate the answer choices:

1. **Option A:**
   - It says that **∠3** is the only exterior angle for remote interior angles **∠1** and **∠2**. This is false because each pair of remote interior angles relates to two different exterior angles. So, **∠4** should also be included as an exterior angle.

2. **Option B:**
   - It correctly states that both **∠1** and **∠2** are the remote interior angles for **∠3** and **∠4**. This matches the correct interpretation of exterior and remote interior angles.

3. **Option C:**
   - It also claims that both **∠1** and **∠2** are remote interior angles for **∠3** and **∠4**, but the diagram is drawn differently from option B. However, this is still a correct statement.

4. **Option D:**
   - Similar to Option A, it claims that **∠3** is the only exterior angle, which is incorrect for the same reason as before.

The correct answers are **Option B** and **Option C**, as both provide correct interpretations of remote interior angles and exterior angles.

Would you like further details on the explanation or have any questions?

Here are 5 questions to expand on this topic:
1. How are exterior angles calculated in a triangle?
2. What is the sum of the exterior angles in any polygon?
3. Can you describe the relationship between the exterior angle and the remote interior angles?
4. How can you prove that the sum of the remote interior angles equals the exterior angle?
5. What happens to the exterior and remote interior angles when the triangle is equilateral?

**Tip:** In any triangle, the exterior angle at one vertex is always equal to the sum of the two remote interior angles.

Marisol claims that each pair of remote interior angles in a triangle has two exterior angles. Do you agree? Use a diagram to support your answer.

Learn how to identify remote interior angles and their corresponding exterior angles in triangles with diagrams. This problem involves analyzing geometric relationships in a triangle using the Exterior Angle Theorem. Suitable for students in Grades 6-8.

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