Answer:
x = 5 1/3
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