+5 In the diagram, quadrilateral ABCD is inscribed in the circle, arc ADB is a minor arc, and segment AB is parallel to segment DC. Given that arc DC is 30 degrees, arc AD is x^2 + 7x degrees, and arc BC is 60 - 4x degrees, find the measure of arc AEB.
https://www.mediafire.com/file/sovz5e8xlsisje1/Screen%20Shot%202017-11-12%20at%208.33.03%20PM.png
(download) (no virus i swear the url says png!!)
[asy]unitsize(2cm);pairA,B,C,D,E;A=dir(170);B=dir(30);D=dir(130);C=dir(70);E=dir(280);draw(Circle((0,0),1));draw(A−−B−−C−−D−−cycle);label("$A$",A,W);label("$B$",B,dir(0));label("$C$",C,NE);label("$D$",D,NW);dot("$E$",E,S);[/asy]
+130466 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°
