Question

look at this diagram: if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle tsq = 133^{circ}$, what is $mangle uvx?$

Explanation:

Step1: Identify vertical - angle relationship

$\angle T S Q$ and $\angle R S V$ are vertical angles. So, $m\angle R S V=m\angle T S Q = 133^{\circ}$.

Step2: Identify corresponding - angle relationship

Since $\overleftrightarrow{R T}$ and $\overleftrightarrow{U W}$ are parallel lines, $\angle R S V$ and $\angle U V X$ are corresponding angles.
For parallel lines, corresponding angles are congruent. So, $m\angle U V X=m\angle R S V$.

Answer:

$133$