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In this image, the problem is asking to match the possible measures of angles \( A \) and \( C \) in a triangle where angle \( B = 50^\circ \), based on the type of triangle given (Acute Triangle, Obtuse Triangle, or Right Triangle). You are given three possible angle pair options: \( (60^\circ, 70^\circ) \), \( (100^\circ, 30^\circ) \), and \( (90^\circ, 40^\circ) \).

### Analysis:
1. **Acute Triangle**: In an acute triangle, all angles are less than \( 90^\circ \). So both \( A \) and \( C \) must also be less than \( 90^\circ \).
   - \( B = 50^\circ \), so \( A + C = 130^\circ \).
   - The only valid pair of \( A \) and \( C \) that keeps both angles acute is \( (60^\circ, 70^\circ) \).
   
2. **Obtuse Triangle**: In an obtuse triangle, one angle must be greater than \( 90^\circ \). Since \( B = 50^\circ \), one of the other angles, either \( A \) or \( C \), must be greater than \( 90^\circ \).
   - The valid pair is \( (100^\circ, 30^\circ) \) where \( A = 100^\circ \), making it an obtuse triangle.

3. **Right Triangle**: In a right triangle, one of the angles must be \( 90^\circ \).
   - The valid pair is \( (90^\circ, 40^\circ) \), where \( A = 90^\circ \), making it a right triangle.

### Correct matches:
- **Acute Triangle**: \( 60^\circ \) and \( 70^\circ \)
- **Obtuse Triangle**: \( 100^\circ \) and \( 30^\circ \)
- **Right Triangle**: \( 90^\circ \) and \( 40^\circ \)

Let me know if you would like further explanation on any part of the reasoning.

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### Follow-up questions:
1. Can you explain how the sum of angles in a triangle is always \( 180^\circ \)?
2. Why can't a triangle have more than one obtuse angle?
3. How do we classify triangles based on their angles?
4. How can we confirm if a given set of angles can form a triangle?
5. What is the relationship between angle measures and side lengths in triangles?

### Tip:
When solving problems involving triangles, always remember that the sum of the interior angles of a triangle is \( 180^\circ \). This can help you quickly verify if angle measures are valid.

In triangle ABC, the measure of angle B is 50 degrees. Match the possible measures for angles A and C based on the type of triangle listed.

Explore how to match the possible measures of angles A and C in triangle ABC, where angle B is 50°. Learn about different triangle types such as acute, obtuse, and right triangles, and apply the Triangle Sum Theorem. Suitable for students in Grades 6-8.

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