Question

BD bisects LABC.Find mZABD, mZCBD, and mZABCA(3x + 6)B17x 18)m_ABD = 0mZCBD =omZABC =|

Answer 1

Bisecting an angle means the angle is divided into half. Therefore,

`m\angle ABD\text{ = }\angle\text{mCBD = }(1)/(2)\angle mABC`
`\begin{gathered} 3x\text{ + 6 = }7x_{}-18\text{ } \\ 3x-7x\text{ = -18 -6} \\ -4x\text{ = -24} \\ x\text{ = }(24)/(4) \\ x\text{ = 6} \end{gathered}`
`\begin{gathered} m\angle ABD\text{ =3x }+\text{ 6 = 3 }*\text{ 6 + 6 = 18 + 6 = 24} \\ m\angle CBD\text{ = 7x }-18\text{ = 7 }*\text{ 6 - 18 = 42 - 18 = 24} \\ m\angle ABC\text{ = 48 } \end{gathered}`