Question

<—> <—> AC and EG are I, and /_FBC is the complement of /_ABD. Find the m/_EBF.

Answer 1

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

`\angle FBC+\angle ABD=90\degree`

Let us substitute the given values and solve for x.

`\begin{gathered} (x+4)+(5x-10)=90 \\ x+5x+4-10=90 \\ 6x-6=90 \\ 6x=90+6 \\ 6x=96 \\ x=(96)/(6) \\ x=16\degree \end{gathered}`

So the angle FBC is

`\begin{gathered} \angle FBC=x+4_{} \\ \angle FBC=16+4 \\ \angle FBC=20\degree \end{gathered}`

Since we know that lines AC and EG are perpendicular so the angle FBC and angle EBF must add up to 90°

`\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}`

Therefore, the angle EBF is 70°.