Both angles are supplementary, as line DB bisects line AC. This means that both angle ABD and angle DBC will add up to 180.
Set up an equation that represents their adding up to 180:
[tex]7x + (x - 4) = 180[/tex]
Simplify the equation:
[tex]7x + x = 8x[/tex]
[tex]8x - 4 = 180[/tex]
Add 4 to both sides:
[tex]8x = 184[/tex]
Divide both sides by 8 to get x by itself:
[tex]x = 23[/tex]
Plug the value of x into the given equation for angle DBC:
[tex]23 - 4 = 19[/tex]
m<DBC is 19 degrees wide.
