You can determine D easily enough to be 114 deg.
You can further determine that this is an isoceles triangle and that AC=BC.
Then you can use the law of sines to get
$\dfrac{\sin(114deg)}{BC}=\dfrac{\sin(48deg)}{DC}$
$\dfrac{\sin(x)}{DC}=\dfrac{\sin(174deg-x)}{AC}$
$\dfrac{\sin(114deg)}{\sin(48deg)}=\dfrac{BC}{DC}= \dfrac{AC}{DC}=\dfrac{\sin(174deg-x)}{\sin(x)}$
You can solve this equation to obtain
Spoiler: