Question

complete the proof that m∠prq + m∠tuw = 180°. 1. (overleftrightarrow{tv}paralleloverleftrightarrow{qs}) given 2. ∠tuw≅∠qru corresponding angles theorem 3. m∠prq + m∠qru = 180° 4. m∠prq + m∠tuw = 180°

Explanation:

Step1: Identify linear - pair angles

$\angle PRQ$ and $\angle QRU$ form a linear - pair. By the Linear - Pair Postulate, if two angles form a linear pair, then they are supplementary. So, $m\angle PRQ + m\angle QRU=180^{\circ}$.

Step2: Substitute $\angle QRU$ with $\angle TUW$

Since $\angle TUW\cong\angle QRU$ (from the Corresponding Angles Theorem), we can substitute $\angle QRU$ with $\angle TUW$ in the equation $m\angle PRQ + m\angle QRU = 180^{\circ}$. So, $m\angle PRQ + m\angle TUW=180^{\circ}$.

Answer:

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