Question

look at this diagram: if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle tsv = 62^{circ}$, what is $mangle tsq$?

Explanation:

Step1: Identify angle - relationship

$\angle TSV$ and $\angle T SQ$ are supplementary angles (a linear - pair of angles).

Step2: Use the supplementary - angle property

The sum of two supplementary angles is $180^{\circ}$. So, $m\angle TSV + m\angle TSQ=180^{\circ}$.

Step3: Solve for $m\angle TSQ$

Given $m\angle TSV = 62^{\circ}$, then $m\angle TSQ=180^{\circ}-m\angle TSV$. Substitute $m\angle TSV = 62^{\circ}$ into the equation: $m\angle TSQ = 180 - 62=118^{\circ}$.

Answer:

$118$