We know that
• BD bisects the angle ABC.
Remember that a bisector divides the angle in two equal parts, that means
[tex]m\angle ABD=m\angle DBC[/tex]
Where,
[tex]m\angle ABD=8x+35,m\angle DBC=11x+23[/tex]
Replacing these expressions we have
[tex]8x+35=11x+23[/tex]
Now, we solve for x, first, we subtract -11x on each side
[tex]\begin{gathered} 8x+35-11x=11x+23-11x \\ -3x+35=23 \end{gathered}[/tex]
Then, we subtract 35 on each side
[tex]\begin{gathered} -3x+35-35=23-35 \\ -3x=-12 \end{gathered}[/tex]
At last, we divide the equation by -3
[tex]\begin{gathered} \frac{-3x}{-3}=\frac{-12}{-3} \\ x=4 \end{gathered}[/tex]
We use this value to find each angle.
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