We are given the following information
Line AC and EG are perpendicular.
Angle FBC is the complement of the angle ABD.
Angle FBC = (x + 4)°
Angle ABD = (5x - 10)°
We are asked to find the angle EBF.
Recall that when two angles are complementary then they add up to 90°
So we can write
[tex]\angle FBC+\angle ABD=90\degree[/tex]
Let us substitute the given values and solve for x.
[tex]\begin{gathered} (x+4)+(5x-10)=90 \\ x+5x+4-10=90 \\ 6x-6=90 \\ 6x=90+6 \\ 6x=96 \\ x=\frac{96}{6} \\ x=16\degree \end{gathered}[/tex]
So the angle FBC is
[tex]\begin{gathered} \angle FBC=x+4_{} \\ \angle FBC=16+4 \\ \angle FBC=20\degree \end{gathered}[/tex]
Since we know that lines AC and EG are perpendicular so the angle FBC and angle EBF must add up to 90°
[tex]\begin{gathered} \angle FBC+\angle EBF=90\degree \\ 20\degree+\angle EBF=90\degree \\ \angle EBF=90\degree-20\degree \\ \angle EBF=70\degree \end{gathered}[/tex]
Therefore, the angle EBF is 70°.
