In reference to the image attached: Is it possible to solve for x despite the fact that I don't know almost anything about the location of point E? If so, how could this be done?
There is not enough information to solve this problem.
However, you can determine a fomula to find x.
Because AB is parallel to CD and AD if parallel to BC, we know that ABCD form a parallelogram.
In a parallelogram, opposite angles are congruent.
`/_` ADC = `/_` ABC
Both angles are equal to x.
We also know ABE is a triangle and the sum of the angles of a triangle is 180 degrees.
Keep in mind that `/_` ABC + `/_` CBE = `/_` ABE
`/_` ABE = x + 20
`/_` EAB + `/_` ABE + `/_` AEB = 180
50 + x + 20 + `/_` AEB = 180
70 + x + `/_` AEB = 180
x + `/_` AEB = 110
x = 110 - `/_` AEB
If you are given the measure of `/_` AEB, you can use the formula above to find x.