Question

Which value of x would make FG II BC?

1
3
6
9

Answer 1

x - 1 x + 1
------ = --------------
x + 3 x + 6

if x = 9
8/ 12 = 10/15

12 (10) = 8(15)
120 = 120

so
answer is 9 (last choice)

Answer 2

Answer: The value of x is 9.

Step-by-step 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,

`\angle GFA=\angle CBA`

`\angle AGF=\angle ACB`

Angle A is common is both triangles.

`(FA)/(BA)= (GA)/(CA)`

`(x+1)/((x+1)+(x+6))= (x-1)/((x-1)+(x+3))`

`(x+1)/((2x+7)= (x-1)/((2x+2))`

`(x+1)(2x+2)=(x-1)(2x+7)`

`2x^2+4x+2=2x^2+5x-7`

`4x+2=5x-7`

`x=9`

Therefore, the value of x is 9.