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To prove that \( m\angle UVX + m\angle QSR = 180^\circ \) based on the diagram, we can use properties of parallel lines and transversals.

### Proof Steps:

1. **Identify corresponding and vertical angles**:  
   In the diagram, lines \( UV \parallel QX \), and line \( RS \) is a transversal. This means that angle \( \angle UVX \) and angle \( \angle QSR \) are supplementary because they form a pair of consecutive interior angles.
   
2. **Statement**: \( m\angle UVX + m\angle QSR = 180^\circ \)  
   **Reason**: Consecutive interior angles formed by parallel lines and a transversal are supplementary.

Thus, the sum of these angles is 180°.

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Would you like more detailed steps on this proof or have any questions? 

Here are 5 follow-up questions that expand on this topic:

1. How do you identify parallel lines and transversals in geometric proofs?
2. What are consecutive interior angles, and why are they supplementary?
3. Can you prove this using alternate interior angles instead?
4. What is the difference between consecutive and alternate angles in geometry?
5. How can you apply this concept to other geometry problems involving parallel lines?

**Tip**: In geometry, always remember that parallel lines cut by a transversal create multiple types of angle relationships, such as corresponding, alternate interior, and consecutive interior angles.

Prove that m∠UVX + m∠QSR = 180° using the diagram with intersecting lines and angles UVX, QSR.

This geometric proof demonstrates how to prove that m∠UVX + m∠QSR = 180° using the properties of parallel lines and transversals. Learn about the Consecutive Interior Angles Theorem and apply it to intersecting lines in this step-by-step solution. Suitable for students in Grades 9-10.

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