Question

look at this diagram: if $overleftrightarrow{su}$ and $overleftrightarrow{vx}$ are parallel lines and $mangle xwt = 123^circ$, what is $mangle stw$?

Explanation:

Step1: Identify angle relationship

Since \( \overleftrightarrow{SU} \parallel \overleftrightarrow{VX} \) and \( \overleftrightarrow{YR} \) is a transversal, \( \angle XWT \) and \( \angle STW \) are same - side interior angles. The sum of same - side interior angles is \( 180^{\circ} \).

Step2: Calculate \( m\angle STW \)

We know that \( m\angle XWT = 123^{\circ} \) and \( m\angle XWT+m\angle STW = 180^{\circ} \). So, \( m\angle STW=180^{\circ}-m\angle XWT \).
Substitute \( m\angle XWT = 123^{\circ} \) into the formula: \( m\angle STW = 180^{\circ}- 123^{\circ}=57^{\circ} \).

Answer:

\( 57^{\circ} \)