In the diagram, points $B$ and $C$ lie on $A D$ and point $E$ lies on $C F$. The measures of four angles are shown. What is the value of $x+y+z$ ?

![](https://cdn.mathpix.com/cropped/2024_04_17_2efeb2001664c4e9869eg-1.jpg?height=429&width=656&top_left_y=1268&top_left_x=797)
Since $\angle F C B$ is an exterior angle for $\triangle E C D$, then $\angle F C B=\angle C E D+\angle E D C=y^{\circ}+z^{\circ}$.

Since $\angle F B A$ is an exterior angle for $\triangle F B C$, then $\angle F B A=\angle B F C+\angle F C B=x^{\circ}+\left(y^{\circ}+z^{\circ}\right)$. Since $\angle F B A=124^{\circ}$, then $124^{\circ}=x^{\circ}+y^{\circ}+z^{\circ}$ or $x+y+z=124$.

ANSWER: 124