Question

look at this diagram? if (overline{tv}) and (overline{wy}) are parallel lines and (mangle xu = 110^{circ}), what is (mangle tux)?

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, meaning they add up to 180°. $\angle{XU}$ and $\angle{TUX}$ form a linear pair.
Let $m\angle{TUX}=x$.
We know that $m\angle{XU} + x=180^{\circ}$.

Step2: Substitute the given angle value

Given $m\angle{XU} = 110^{\circ}$.
Substitute into the equation: $110^{\circ}+x = 180^{\circ}$.
Solve for $x$: $x=180^{\circ}-110^{\circ}$.
$x = 70^{\circ}$.

Answer:

$70^{\circ}$