Question

complete the proof that ( mangle ruv + mangle sru = 180^{circ} ).

1 ( overleftrightarrow{qs} parallel overleftrightarrow{tv} ) given
2 ( angle ruv cong angle prs ) corresponding angles theorem
3 ( mangle prs + mangle sru = 180^{circ} ) angles forming a linear pair sum to ( 180^{circ} )
4

Explanation:

Step1: Substitute angles

Since \(\angle RUV\cong\angle PRS\) (from step 2), we can substitute \(\angle PRS\) with \(\angle RUV\) in the equation \(m\angle PRS + m\angle SRU=180^{\circ}\) (from step 3).

Answer:

\(m\angle RUV + m\angle SRU = 180^{\circ}\) (by substitution property of equality)