Question

look at this diagram:
if \\( \overleftrightarrow { s u } \\) and \\( \overleftrightarrow { v x } \\) are parallel lines and \\( m \angle s t w = 42 ^ { \circ } \\), what is \\( m \angle x w t \\)?

Explanation:

Step1: Identify the relationship between angles

$\overrightarrow{SU}$ and $\overrightarrow{VX}$ are parallel lines. $\angle STW$ and $\angle XWT$ are same - side interior angles.

Step2: Use the property of same - side interior angles

The sum of same - side interior angles is $180^{\circ}$. So, $m\angle STW+m\angle XWT = 180^{\circ}$.

Step3: Solve for $m\angle XWT$

Given $m\angle STW = 42^{\circ}$, then $m\angle XWT=180^{\circ}-m\angle STW$. Substitute the value: $m\angle XWT = 180 - 42=138^{\circ}$.

Answer:

$138$