Question

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

Explanation:

Step1: Recall given and previous - derived facts

We are given $\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}$, and we know $\angle SVU\cong\angle QSR$ (Corresponding Angles Theorem) and $m\angle QSR + m\angle RSV=180^{\circ}$ (linear - pair property).

Step2: Use substitution

Since $\angle SVU\cong\angle QSR$, then $m\angle SVU = m\angle QSR$. 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:

Substitution