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 m∠rsv+m∠svu=180°

Explanation:

Step1: Identify given information

$\overleftrightarrow{RT}\parallel\overleftrightarrow{UW}$ (Given)

Step2: Use corresponding - angles theorem

Since $\overleftrightarrow{RT}\parallel\overleftrightarrow{UW}$, $\angle SVU\cong\angle QSR$ (Corresponding Angles Theorem)

Step3: Consider linear - pair of angles

$\angle QSR$ and $\angle RSV$ form a linear pair, so $m\angle QSR + m\angle RSV=180^{\circ}$ (Angles forming a linear pair sum to $180^{\circ}$)

Step4: Substitute equal angles

Since $\angle SVU\cong\angle QSR$, then $m\angle SVU = m\angle QSR$. Substituting $m\angle QSR$ with $m\angle SVU$ in $m\angle QSR + m\angle RSV = 180^{\circ}$, we get $m\angle RSV + m\angle SVU=180^{\circ}$

Answer:

The proof is completed as shown above. The key steps are using the given parallel - line condition, corresponding - angles theorem, linear - pair property, and substitution.