Question

look at this diagram: if \\( \overleftrightarrow { rt } \\) and \\( \overleftrightarrow { uw } \\) are parallel lines and \\( m\angle t s q = 110 ^ { \circ } \\), what is \\( m\angle w v x \\)?

Explanation:

Step1: Identify vertical angles

$\angle TSQ$ and $\angle RSV$ are vertical angles, so $m\angle RSV = m\angle TSQ = 110^\circ$.

Step2: Find consecutive interior angle

$\angle RSV$ and $\angle WVX$ are consecutive interior angles (since $RT \parallel UW$), so they are supplementary:
$m\angle RSV + m\angle WVX = 180^\circ$.

Step3: Calculate $m\angle WVX$

$m\angle WVX = 180^\circ - 110^\circ = 70^\circ$.

Answer:

70