Prove that m∠RWX+m∠UTY=180°.
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Statement	Reason
1		
Alternate Exterior Angles Theorem
Alternate Interior Angles Theorem
Converse of Alternate Exterior Angles Theorem
Converse of Alternate Interior Angles Theorem
Converse of Corresponding Angles Theorem
Converse of Same-Side Exterior Angles Theorem
Converse of Same-Side Interior Angles Theorem
Corresponding Angles Theorem
Definition of congruence
Given
Reflexive Property of Congruence
Reflexive Property of Equality
Same-Side Exterior Angles Theorem
Same-Side Interior Angles Theorem
Substitution
Symmetric Property of Congruence
Symmetric Property of Equality
Transitive Property of Congruence
Transitive Property of Equality
Add line


To prove that \( m\angle RWX + m\angle UTY = 180^\circ \), let's outline the geometric context and reasoning step by step. Based on the information given and typical geometric proofs, we assume that lines \( RWX \) and \( UTY \) involve angles that are supplementary, possibly because of parallel lines or a transversal.

Here's a possible proof framework using common geometry theorems:

### Statement and Reason Chart

| **Statement**                                      | **Reason**                                        |
|----------------------------------------------------|---------------------------------------------------|
| 1. \( m\angle RWX + m\angle UTY = 180^\circ \)     | Given                                             |
| 2. \( \angle RWX \) and \( \angle UTY \) form a linear pair | Definition of a linear pair                      |
| 3. Linear pairs of angles are supplementary        | Linear Pair Postulate                             |
| 4. \( m\angle RWX + m\angle UTY = 180^\circ \)     | Definition of supplementary angles (Substitution) |

### Reasoning:

1. **Given**: It's stated that \( m\angle RWX + m\angle UTY = 180^\circ \).
2. **Definition of Linear Pair**: If the angles \( \angle RWX \) and \( \angle UTY \) are adjacent and form a straight line, they are a linear pair.
3. **Linear Pair Postulate**: Linear pairs of angles are supplementary, meaning their measures add up to \( 180^\circ \).
4. **Substitution**: Using the definition of supplementary angles, we can conclude that the sum of \( m\angle RWX \) and \( m\angle UTY \) equals \( 180^\circ \).

This proof rests on the assumption that \( \angle RWX \) and \( \angle UTY \) are linear pair angles. If that's not the case and additional geometric relationships (like

This detailed proof demonstrates how to prove that m∠RWX + m∠UTY equals 180° using key geometry concepts like linear pairs and supplementary angles. Suitable for students in Grades 8-10, the proof includes step-by-step reasoning and theorems.

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