Question

look at this diagram: if (overleftrightarrow{tv}) and (overleftrightarrow{wy}) are parallel lines and (mangle tux = 132^{circ}), what is (mangle vux?)

Explanation:

Step1: Identify angle - relationship

$\angle TUX$ and $\angle VUX$ 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 $m\angle VUX = x$. We know that $m\angle TUX=132^{\circ}$, and $m\angle TUX + m\angle VUX=180^{\circ}$. So, $x = 180^{\circ}-m\angle TUX$.

Step3: Calculate the angle measure

Substitute $m\angle TUX = 132^{\circ}$ into the formula: $x=180 - 132=48^{\circ}$.

Answer:

$48$