Question

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

Explanation:

Step1: Given

This is usually the starting - point of a proof. We assume $\overleftrightarrow{UW}\parallel\overleftrightarrow{RT}$ as given information.

Step2: Corresponding angles postulate

If two parallel lines ($\overleftrightarrow{UW}$ and $\overleftrightarrow{RT}$) are cut by a transversal, then corresponding angles are congruent. So, $\angle WVX\cong\angle TSV$.

Step3: Linear - pair postulate

$\angle QST$ 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 $m\angle QST + m\angle TSV=180^{\circ}$.

Step4: Substitution property

Since $\angle WVX\cong\angle TSV$, then $m\angle WVX = m\angle TSV$. Substituting $m\angle WVX$ for $m\angle TSV$ in the equation $m\angle QST + m\angle TSV = 180^{\circ}$, we get $m\angle QST + m\angle WVX=180^{\circ}$.

Answer:

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