Answer
$m\angle ABC=45$
$m\angle DBC=34$
Work Step by Step
Angle Addition Postulate:
$m\angle ABC + m\angle DBC =m\angle ABD$
Substitute the given values.
$(8x-3)+(5x+4)=79$
Solve for x.
Combine like values.
$13x+1=79$
Subtract 1 from each side.
$13x+1-1=79-1$
$13x=78$
Divide each side by 13.
$13x\div13=78\div13$
$x=6$
Substitute for x to find $m\angle ABC$
$m\angle ABC=8x-3=8(6)-3=48-3=45$
Substitute for x to find $m\angle DBC$
$m\angle DBC=5x+4=5(6)+4=30+4=34$
