In the diagram, $A B$ is parallel to $C D$. Points $E$ and $F$ are on $A B$ and $C D$, respectively, so that $\angle F A B=30^{\circ}$ and $\angle A F E=\angle E F B=\angle B F D=x^{\circ}$. What is the value of $x$ ?

![](https://cdn.mathpix.com/cropped/2024_04_17_5042e00a68bea6f5e8e9g-1.jpg?height=290&width=545&top_left_y=1107&top_left_x=1359)
Since $A B$ and $C D$ are parallel, then $\angle B A F$ and $\angle A F D$ are co-interior angles.

Therefore, $\angle B A F+\angle A F D=180^{\circ}$, and so $30^{\circ}+3 x^{\circ}=180^{\circ}$.

This gives $3 x=150$ or $x=50$.

ANSWER: 50