Question

help please. I'm not sure how to do this and there's no material in my book that explains how to do it either

Answer 1

We know that

• BD bisects the angle ABC.

Remember that a bisector divides the angle in two equal parts, that means

`m\angle ABD=m\angle DBC`

Where,

`m\angle ABD=8x+35,m\angle DBC=11x+23`

Replacing these expressions we have

`8x+35=11x+23`

Now, we solve for x, first, we subtract -11x on each side

`\begin{gathered} 8x+35-11x=11x+23-11x \\ -3x+35=23 \end{gathered}`

Then, we subtract 35 on each side

`\begin{gathered} -3x+35-35=23-35 \\ -3x=-12 \end{gathered}`

At last, we divide the equation by -3

`\begin{gathered} (-3x)/(-3)=(-12)/(-3) \\ x=4 \end{gathered}`

We use this value to find each angle.