Questions: S U is parallel to V X. Complete the proof that m angle RTS + m angle VWY = 180°. 1. S U is parallel to V X - Given 2. angle VWY is congruent to angle STW 3. m angle RTS + m angle STW = 180° 4. m angle RTS + m angle VWY = 180°

S U is parallel to V X. Complete the proof that m angle RTS + m angle VWY = 180°. 1. S U is parallel to V X - Given 2. angle VWY is congruent to angle STW 3. m angle RTS + m angle STW = 180° 4. m angle RTS + m angle VWY = 180°
Transcript text: $\overleftrightarrow{S U} \| \overleftrightarrow{V X}$. Complete the proof that $m \angle R T S+m \angle V W Y=180^{\circ}$. \begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $\overleftrightarrow{S U} \| \overleftrightarrow{V X}$ & Given \\ 2 & $\angle V W Y \cong \angle S T W$ & \\ 3 & $m \angle R T S+m \angle S T W=180^{\circ}$ & \\ 4 & $m \angle R T S+m \angle V W Y=180^{\circ}$ & \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Reason for Statement 2

Since $\overleftrightarrow{S U}$ is parallel to $\overleftrightarrow{V X}$, angles $\angle V W Y$ and $\angle S T W$ are corresponding angles. Therefore, $\angle V W Y \cong \angle S T W$ due to the Corresponding Angles Postulate.

Step 2: Reason for Statement 3

Angles $\angle RTS$ and $\angle STW$ are adjacent angles that form a straight line. Therefore, they are supplementary angles, meaning $m\angle RTS + m\angle STW = 180^\circ$.

Step 3: Reason for Statement 4

Since $\angle V W Y \cong \angle S T W$, their measures are equal: $m\angle VWY = m\angle STW$. Substituting this into the equation from Step 2 ($m\angle RTS + m\angle STW = 180^\circ$) gives $m\angle RTS + m\angle VWY = 180^\circ$.

Final Answer

\begin{tabular}{|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $\overleftrightarrow{S U} \| \overleftrightarrow{V X}$ & Given \\ 2 & $\angle V W Y \cong \angle S T W$ & Corresponding Angles Postulate \\ 3 & $m \angle R T S+m \angle S T W=180^{\circ}$ & Supplementary Angles \\ 4 & $m \angle R T S+m \angle V W Y=180^{\circ}$ & Substitution Property of Equality \\ \hline \end{tabular}

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