Question

complete the proof that m∠wvx + m∠qst = 180°. statement reason 1. (overleftrightarrow{rt}paralleloverleftrightarrow{uw}) given 2. ∠wvx≅∠tsv 3. m∠qst + m∠tsv = 180° 4. m∠wvx + m∠qst = 180° substitution

Explanation:

Step1: Identify angle - relationship for parallel lines

When two parallel lines ($\overleftrightarrow{RT}\parallel\overleftrightarrow{UW}$) are cut by a transversal ($\overleftrightarrow{XU}$), $\angle WVX$ and $\angle TSV$ are corresponding angles. By the Corresponding Angles Postulate, corresponding angles are congruent. So the reason for $\angle WVX\cong\angle TSV$ is "Corresponding Angles Postulate".

Step2: Identify angle - relationship for a linear pair

$\angle QST$ and $\angle TSV$ form a linear pair. By the Linear - Pair Postulate, the sum of the measures of two angles in a linear pair is $180^{\circ}$. So the reason for $m\angle QST + m\angle TSV=180^{\circ}$ is "Linear - Pair Postulate".

Answer:

1. Corresponding Angles Postulate
2. Linear - Pair Postulate