Question

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

Explanation:

Step1: Recall angle - congruence property

Since $\angle SVU\cong\angle QSR$, their measures are equal, i.e., $m\angle SVU = m\angle QSR$.

Step2: Substitute equal - measure angles

We know that $m\angle QSR + m\angle RSV=180^{\circ}$. Substituting $m\angle SVU$ for $m\angle QSR$ (because $m\angle SVU = m\angle QSR$ from step 1), we get $m\angle RSV + m\angle SVU = 180^{\circ}$.

Answer:

$m\angle RSV + m\angle SVU = 180^{\circ}$