Question

Let BD bisect LABC. If m_ABD =(2x+5)" and mzDBC=\X47), then what is the mesure d 0809 Z B

Answer 1

Remember that an angle bisector divides the angle into two equal parts, this definition allows us to express the following equivalence.

`m\angle ABD=m\angle DBC`

Let's replace the expressions.

`2x+5=x+7`

Now, we solve for x.-

`\begin{gathered} 2x-x=7-5 \\ x=2 \end{gathered}`

We use this value to find angle ABD.

`m\angle ABD=2x+5=2(2)+5=4+5=9`

Therefore, angle ABD is equal to 9°.