Question

complete the proof that (mangle qst + mangle wvx = 180^{circ}).
statement
1 (overleftrightarrow{uw}paralleloverleftrightarrow{rt})
2 (angle wvxcongangle tsv)
3 (mangle qst + mangle tsv = 180^{circ})
4 (mangle qst + mangle wvx = 180^{circ})
reason

Explanation:

Step1: Given parallel lines

Given that $\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}$.

Step2: Corresponding - angles postulate

Since $\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}$, by the corresponding - angles postulate, $\angle WVX\cong\angle TSV$, so $m\angle WVX = m\angle TSV$.

Step3: Linear - pair postulate

$\angle QST$ and $\angle TSV$ form a linear pair. By the linear - pair postulate, $m\angle QST + m\angle TSV=180^{\circ}$.

Step4: Substitution property

Since $m\angle WVX = m\angle TSV$, we substitute $m\angle TSV$ with $m\angle WVX$ in the equation $m\angle QST + m\angle TSV = 180^{\circ}$, getting $m\angle QST + m\angle WVX=180^{\circ}$.

Answer:

1. Given
2. Corresponding - angles postulate
3. Linear - pair postulate
4. Substitution property