Geometry-10th Grade-Paralellograms can you solve for x?(25 points)

x = 5 1/3

Step-by-step explanation:

AD // BK

∠DAk ≅ ∠BKA  ≅ ∠KAB     ∴ AB = 10 = BK = BC + CK = 6 + CK

∴ CK = 4

ΔKFC similar to ΔAFD   (AAA)

KC / KD = KF / (FE + EA)        4/6 = 2/3 = x / (3 + y)

3x = 6 + 2y --- (1)

ΔAED similar to ΔKEB   (AAA)

AE / EK = AD / BK        y / (3 + x) = 6 / 10 = 3 / 5

3x + 9 = 5y          3x = 5y - 9-------- (2)

6 + 2y = 5y - 9

3y = 15        y = 5

x = (5 x 5 - 9) /3 = 16/3 = 5 1/3