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 - type relationship

$\angle UVX$ and $\angle TSV$ are corresponding angles. Since $\overleftrightarrow{RT}$ and $\overleftrightarrow{UW}$ are parallel lines, corresponding angles are equal. So $m\angle TSV=m\angle UVX = 114.2^{\circ}$.

Step2: Note linear - pair relationship

$\angle TSV$ and $\angle TSQ$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle TSV + m\angle TSQ=180^{\circ}$.

Step3: Solve for $m\angle TSQ$

$m\angle TSQ=180^{\circ}-m\angle TSV$. Substitute $m\angle TSV = 114.2^{\circ}$ into the equation: $m\angle TSQ=180 - 114.2=65.8^{\circ}$.

Answer:

$65.8$