Angle Sum Proof 266338

1. **State the problem:** We need to prove that $m\angle PRS + m\angle VUW = 180^\circ$ given the parallel lines and angle relationships. 2. **Given information:** - $XZ \parallel QS$ - $XZ \parallel TV$ - $\angle VUW \cong \angle WYZ$ - $m\angle WYZ + m\angle PRS = 180^\circ$ 3. **Recall the substitution property:** If two angles are congruent, their measures are equal. So, $m\angle VUW = m\angle WYZ$ 4. **Use substitution in the equation:** Given: $m\angle WYZ + m\angle PRS = 180^\circ$ Substitute $m\angle VUW$ for $m\angle WYZ$: $$m\angle PRS + m\angle VUW = 180^\circ$$ 5. **Conclusion:** We have shown that the sum of the measures of angles $PRS$ and $VUW$ is $180^\circ$ by substitution, completing the proof.