Question

uw || rt. complete the proof that m∠svu + m∠rsv = 180°. statement reason 1 uw || rt given 2 ∠svu ≅ ∠qsr corresponding angles theorem 3 m∠qsr + m∠rsv = 180° 4 m∠svu + m∠rsv = 180°

Explanation:

Step1: Identify linear - pair angles

$\angle QSR$ and $\angle RSV$ form a linear - pair. By the Linear - Pair Postulate, if two angles form a linear - pair, then the sum of their measures is $180^{\circ}$. So, $m\angle QSR + m\angle RSV=180^{\circ}$.

Step2: Use angle - congruence substitution

Since $\angle SVU\cong\angle QSR$ (from step 2, Corresponding Angles Theorem), then $m\angle SVU = m\angle QSR$ (congruent angles have equal measures). Substituting $m\angle SVU$ for $m\angle QSR$ in the equation $m\angle QSR + m\angle RSV = 180^{\circ}$, we get $m\angle SVU + m\angle RSV=180^{\circ}$.

Answer:

1. Linear - Pair Postulate; 4. Substitution Property of Equality