Question

$\overleftrightarrow{tv} \parallel \overleftrightarrow{wy}$. complete the proof that $m\angle wxz + m\angle sut = 180^\circ$.

	statement	reason
1	$\overleftrightarrow{tv} \parallel \overleftrightarrow{wy}$	given
2	$\angle wxz \cong \angle tux$
3	$m\angle sut + m\angle tux = 180^\circ$
4	$m\angle wxz + m\angle sut = 180^\circ$

Explanation:

Step1: Reason for Statement 2

When two parallel lines (\(\overleftrightarrow{TV} \parallel \overleftrightarrow{WY}\)) are cut by a transversal (\(\overleftrightarrow{SZ}\)), the corresponding angles are congruent. So \(\angle WXZ\) and \(\angle TUX\) are corresponding angles, hence \(\angle WXZ \cong \angle TUX\) by the Corresponding Angles Theorem.

Step2: Reason for Statement 3

\(\angle SUT\) and \(\angle TUX\) form a linear pair (they are adjacent angles that form a straight line), so their measures add up to \(180^\circ\) by the Linear Pair Postulate (Linear pairs are supplementary).

Step3: Reason for Statement 4

Since \(\angle WXZ \cong \angle TUX\), we can substitute \(m\angle WXZ\) for \(m\angle TUX\) in the equation \(m\angle SUT + m\angle TUX = 180^\circ\) (Substitution Property of Equality). This gives \(m\angle WXZ + m\angle SUT = 180^\circ\).

Answer:

• Statement 2 Reason: Corresponding Angles Theorem (or Corresponding Angles are Congruent when lines are parallel)
• Statement 3 Reason: Linear Pair Postulate (Linear pairs are supplementary)
• Statement 4 Reason: Substitution Property of Equality