Answer:
[tex]x=22[/tex]
Step-by-step explanation:
Because [tex]\angle ABC=\angle ABD+\angle DBC=80^{\circ}[/tex], we have that [tex](2x+4)+(2x-12)=80[/tex].
Combining like terms on the left side gives [tex]4x-8=80[/tex].
Adding [tex]8[/tex] to both sides gives [tex]4x=88[/tex].
Dividing both sides of the equation by [tex]4[/tex] gives [tex]\boxed{x=22}[/tex].
