Answer:
x = 132 degrees
Explanation:
To help explain, lets add some letters to designate those line intersections.
Starting at x, label that intersection O, then go up-right to that intersection and label that P, then go down-right to that intersection and label that Q, then go up-right and name that R, then go down-right and label that S, finally go right to that intersection and label that T.
Angle TRS = 12 degrees because isosceles triangle so TRS = a = 12 degrees.
Angle RST = 180-12-12 = 156 degrees.
Angle QSR is supplementary to RST so it is 24 degrees.
Angle RQS = 24 degrees because isosceles.
Angle QRS = 180-24-24 = 132 degrees.
Angle PRQ = 180-12-132 = 36 degrees.
Angle PRQ = 36 degrees because isosceles.
Angle PQR = 180-36-36 = 108 degrees.
Angle PQO = 180-24-108 = 48 degrees.
Angle POQ = 48 degrees because isosceles.
Angle x = 180 -48 = 132 degrees because it is supplementary.