Variant 9.5.4. Sides $A D$ and $D C$ of the inscribed quadrilateral $A B C D$ are equal. A point $X$ is marked on side $B C$ such that $A B = B X$. It is known that $\angle B = 38^{\circ}$ and $\angle X D C = 54^{\circ}$.

(a) (1 point) How many degrees does the angle $A X C$ measure?

(b) (3 points) How many degrees does the angle $A C B$ measure?

![](https://cdn.mathpix.com/cropped/2024_05_06_1f4981519479532effc1g-13.jpg?height=313&width=703&top_left_y=1483&top_left_x=369)
Answer: (a) $109^{\circ}$. (b) $44^{\circ}$.