Answer:
x = <u>132</u> degrees
Step-by-step 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 = <u>132</u> degrees.
Angle PRQ = 180-12-<u>132</u> = <u>36</u> degrees.
Angle PRQ = <u>36</u> degrees because isosceles.
Angle PQR = 180-<u>36</u>-<u>36</u> = <u>108</u> degrees.
Angle PQO = 180-24-<u>108</u> = <u>48</u> degrees.
Angle POQ = <u>48</u> degrees because isosceles.
Angle x = 180 -<u>48</u> = <u>132</u> degrees because it is supplementary.
