Question

look at this diagram: if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle uvx = 114.2^{circ}$, what is $mangle tsq$?

Explanation:

Step1: Identify angle - relationship

$\angle UVX$ and $\angle RSV$ are vertical angles. Vertical angles are equal. So $m\angle RSV=m\angle UVX = 114.2^{\circ}$.

Step2: Use parallel - line property

Since $\overleftrightarrow{RT}$ and $\overleftrightarrow{UW}$ are parallel lines, $\angle RSV$ and $\angle TSQ$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So $m\angle TSQ=m\angle RSV$.

Answer:

$114.2$