The angle ABD is equal to the sum of the angles ABC and DBC:
So:
ABD=ABC+DBC
Where:
ABD=75
ABC=5x+4
DBC=8x-7
Hence:
75=5x+4+8x-7
Add like terms:
75=13x-3
Add 3 to both sides:
75+3=13x-3+3
78=13x
Divide both sides by 13:
78/13=13x/13
6=x
or
x=6
Now, replace the value of x into ABC and DBC:
ABC=5x+4=5(6)+4=30+4=34
DBC=8x-7=8(6)-7=48-7=41
Therefore:
ABC=34°
DBC=41°
You can verify the result:
ABD=ABC+DBC
75=41+34=75