Question

look at this diagram: if (overleftrightarrow{tv}) and (overleftrightarrow{wy}) are parallel lines and (mangle tux = 134^{circ}), what is (mangle yxu?)

Explanation:

Step1: Recall angle - relationship

$\angle TUX$ and $\angle YXU$ are supplementary angles since $\overleftrightarrow{TV}$ and $\overleftrightarrow{WY}$ are parallel lines and $\overleftrightarrow{ZS}$ is a transversal. Supplementary angles add up to $180^{\circ}$.

Step2: Calculate $\angle YXU$

Let $m\angle YXU=x$. We know that $m\angle TUX + x=180^{\circ}$. Given $m\angle TUX = 134^{\circ}$, then $x = 180^{\circ}-m\angle TUX$.
$x=180 - 134$.
$x = 46^{\circ}$.

Answer:

$46$