Complete the proof that m∠RSV+m∠SVU=180°.
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Statement	Reason
1	
UW
∥
RT
Given
2	∠SVU≅∠QSR	Corresponding Angles Theorem. IXL CUV. Add more proofs if required

Let's complete the proof that \( m\angle RSV + m\angle SVU = 180^\circ \) given that \( UW \parallel RT \).

### Proof:
| **Statement** | **Reason** |
|---------------|------------|
| 1. \( UW \parallel RT \) | Given |
| 2. \( \angle SVU \cong \angle QSR \) | Corresponding Angles Theorem (angles formed by a transversal intersecting two parallel lines are congruent) |
| 3. \( m\angle SVU = m\angle QSR \) | Definition of congruent angles |
| 4. \( m\angle RSV + m\angle QSR = 180^\circ \) | Linear Pair Postulate (angles that form a straight line add up to 180°) |
| 5. \( m\angle RSV + m\angle SVU = 180^\circ \) | Substitution (replace \( m\angle QSR \) with \( m\angle SVU \) from step 3) |

### Conclusion:
The proof is complete, showing that \( m\angle RSV + m\angle SVU = 180^\circ \) by using the Corresponding Angles Theorem and the Linear Pair Postulate.

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Would you like more details or have any questions?

### Related Questions:
1. What is the Corresponding Angles Theorem?
2. How does the Linear Pair Postulate work in different scenarios?
3. Can you provide examples of the Substitution property in proofs?
4. What are other angle theorems related to parallel lines and transversals?
5. How can you prove that two lines are parallel using angles?

### Tip:
Always remember that when two lines are parallel and cut by a transversal, corresponding angles are equal, which is a key concept in many geometric proofs.

Learn how to complete the proof that the sum of angles m∠RSV and m∠SVU equals 180 degrees using the Corresponding Angles Theorem and the Linear Pair Postulate. Understand the concept of congruent angles formed by parallel lines and a transversal. Suitable for high school students studying geometry.

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