Variant 9.5.1. 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 $\angle B = 34^{\circ}$ and $\angle X D C = 52^{\circ}$.

(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-12.jpg?height=313&width=693&top_left_y=1357&top_left_x=380)
Answer: (a) $107^{\circ}$. (b) $47^{\circ}$.