Answer:
FG = 31
Explanation:
By applying mid-segment theorem in the given trapezoid,
Segment joining midpoints of the nonparallel sides is parallel and measure the half of the sum of parallel sides.
FG =
![(1)/(2)[UV+TW]](https://img.qammunity.org/2022/formulas/mathematics/college/317namp9nxl0c5quro6c4f930gxsbnws9f.png)
(7x - 4) =
![(1)/(2)[(6x-6)+38]](https://img.qammunity.org/2022/formulas/mathematics/college/svv68kyq44y6ahw21fim4p5bdrneg38u3z.png)
2(7x - 4) = 6x + 32
14x - 8 = 6x + 32
14x - 6x = 32 + 8
8x = 40
x = 5
Therefore, FG = (7x - 4)
= 7(5) - 4
= 31