Question

look at this diagram: if (overleftrightarrow{tv}) and (overleftrightarrow{wy}) are parallel lines and (mangle wxu = 113^{circ}), what is (mangle tux)?

Explanation:

Step1: Identify angle - relationship

$\angle WXU$ and $\angle TUX$ are supplementary angles since $\overleftrightarrow{TV}$ and $\overleftrightarrow{WY}$ are parallel lines and $ZS$ is a transversal.

Step2: Use the supplementary - angle formula

The sum of supplementary angles is $180^{\circ}$. Let $m\angle TUX = x$. Then $m\angle WXU+x = 180^{\circ}$. Given $m\angle WXU = 113^{\circ}$, we have $x=180^{\circ}-m\angle WXU$.

Step3: Calculate the angle measure

$x = 180 - 113=67^{\circ}$.

Answer:

$67$