The two angles are supplementary; therefore, they should add up to 180 degrees and we have the equation
[tex](7x+1)+(9x-7)=180^o[/tex][tex]16x-6=180[/tex][tex]16x=186[/tex][tex]x=11.625[/tex]Having the value of x in hand, we now put it into the equation for BDC to find its measure.
[tex]\measuredangle BDC=7x+1[/tex][tex]\measuredangle BDC=7(11.625)+1[/tex][tex]\measuredangle BDC=32.375^o[/tex]