Question

look at this diagram: if $overleftrightarrow{tv}$ and $overleftrightarrow{wy}$ are parallel lines and $mangle tux = 129^{circ}$, what is $mangle yxu$?

Explanation:

Step1: Identify angle - type relationship

$\angle TUX$ and $\angle YXU$ are supplementary angles (linear - pair of angles formed by two intersecting lines where $\overleftrightarrow{WY}$ and $\overleftrightarrow{SV}$ intersect at $X$).

Step2: Use the supplementary - angle property

The sum of supplementary angles is $180^{\circ}$. Let $m\angle TUX = 129^{\circ}$ and $m\angle YXU=x$. Then $x + 129^{\circ}=180^{\circ}$.

Step3: Solve for the unknown angle

$x=180^{\circ}- 129^{\circ}=51^{\circ}$.

Answer:

$51$