Since AB is parallel to BC, then chords AD and BC are equal....thus
x^2 + 7x = 60 - 4x rearrange as
x^2 + 11x - 60 = 0 factor
(x - 4) ( x + 15) = 0 setting each factor to 0 and solving for x we have that
x = 4 or x = -15
Taking the positive solution, then BC = AB = 60 - 4(4) = 60 - 16 = 44
Thus arcs AD + DC + CB = [ 44 + 30 + 44 ] = 118°
Thus arc AEB = 360 - 118 = 242°