Bisecting an angle means the angle is divided into half. Therefore,
[tex]m\angle ABD\text{ = }\angle\text{mCBD = }\frac{1}{2}\angle mABC[/tex][tex]\begin{gathered} 3x\text{ + 6 = }7x_{}-18\text{ } \\ 3x-7x\text{ = -18 -6} \\ -4x\text{ = -24} \\ x\text{ = }\frac{24}{4} \\ x\text{ = 6} \end{gathered}[/tex][tex]\begin{gathered} m\angle ABD\text{ =3x }+\text{ 6 = 3 }\times\text{ 6 + 6 = 18 + 6 = 24} \\ m\angle CBD\text{ = 7x }-18\text{ = 7 }\times\text{ 6 - 18 = 42 - 18 = 24} \\ m\angle ABC\text{ = 48 } \end{gathered}[/tex]
