Explanation:
BD² = 3² + 6² = 9 + 36 = 45
BD = sqrt(45) = sqrt(9×5) = 3×sqrt(5)
BX = DX = CX = EX = BD/2 = 3/2 × sqrt(5)
AX² + BX² = 7²
AX² + (3/2 × sqrt(5))² = 49
AX² + 9/4 × 5 = 49
AX² = 196/4 - 45/4 = 151/4
AX = sqrt(151)/2
the requested angle is actually the angle ABX.
the law of sines :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being opposite of the angles.
so,
7/sin(X = 90) = AX/sin(B)
sin(B) × 7 = AX × sin(90) = AX
sin(B) = AX/7 = sqrt(151)/2 / 7 = sqrt(151)/14
angle ABX = 61.36961352...°