Answer: The value of x is 9.
Explanation:
It is given that FG || BC.
If a transversal line intersect two parallel lines then the corresponding angles are same. There in triangle ACB and AGF,
[tex]\angle GFA=\angle CBA[/tex]
[tex]\angle AGF=\angle ACB[/tex]
Angle A is common is both triangles.
[tex]\frac{FA}{BA}= \frac{GA}{CA}[/tex]
[tex]\frac{x+1}{(x+1)+(x+6)}= \frac{x-1}{(x-1)+(x+3)}[/tex]
[tex]\frac{x+1}{(2x+7}= \frac{x-1}{(2x+2)}[/tex]
[tex](x+1)(2x+2)=(x-1)(2x+7)[/tex]
[tex]2x^2+4x+2=2x^2+5x-7[/tex]
[tex]4x+2=5x-7[/tex]
[tex]x=9[/tex]
Therefore, the value of x is 9.
