What thefuc is going on

The measures of angles ADB and BDC add up to the measure of angle ADC:
[tex]134^\circ=(5x+4)^\circ+(7x-2)^\circ[/tex]
[tex]\implies134=12x+2[/tex]
[tex]\implies12x=132[/tex]
[tex]\implies x=11[/tex]
Then
[tex]m\angle BDC=(7\cdot11-2)^\circ=\boxed{75^\circ}[/tex]