Question

look at this diagram: if (overleftrightarrow{rt}) and (overleftrightarrow{uw}) are parallel lines and (mangle wvx = 54^{circ}), what is (mangle tsy)?

Explanation:

Step1: Identify angle - relationship

$\angle{WVX}$ and $\angle{TSQ}$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.

Step2: Use the given angle measure

Since $\angle{WVX}=54^{\circ}$ and $\angle{TSQ}$ is congruent to $\angle{WVX}$, then $m\angle{TSQ} = 54^{\circ}$.

Answer:

$54^{\circ}$