Question

look at this diagram: if $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines and $mangle rsq = 64^{circ}$, what is $mangle tsq$?

Explanation:

Step1: Recall linear - pair property

$\angle RSQ$ and $\angle TSQ$ form a linear - pair. The sum of the measures of angles in a linear - pair is $180^{\circ}$.

Step2: Set up the equation

Let $m\angle TSQ=x$. We know that $m\angle RSQ + m\angle TSQ=180^{\circ}$, and $m\angle RSQ = 64^{\circ}$. So, $64^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-64^{\circ}$.
$x = 116^{\circ}$.

Answer:

$116$