Question

if (overleftrightarrow{tv}) and (overleftrightarrow{wy}) are parallel lines and (mangle wxz = 134^{circ}), what is (mangle yxz?)

Explanation:

Step1: Recall angle - relationship

$\angle WXZ$ and $\angle YXZ$ are supplementary angles since they form a linear - pair.

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle YXZ = x$. Then $m\angle WXZ+x = 180^{\circ}$. Given $m\angle WXZ = 134^{\circ}$, we have $134^{\circ}+x = 180^{\circ}$.

Step3: Solve for $x$

$x=180^{\circ}-134^{\circ}=46^{\circ}$.

Answer:

$46$