We can start by using the fact that AABC is an isosceles triangle to find the measure of angle AAB:
mAA + mAB + mAC = 180 (sum of angles in a triangle)
Since AABC is isosceles, we know that angle AAB is congruent to angle AAC:
mAA = mAC
Substituting this into the equation above, we get:
mAA + mAB + mAA = 180
2mAA + mAB = 180
Simplifying, we get:
mAB = 180 - 2mAA
Next, we can use the given angle measures to set up an equation involving angle ABZ:
mABZ = mAB - m5 - mZB
Substituting the given angle measures, we get:
mABZ = (180 - 2mAA) - (1.5x + 17) - (5x - 9)
Simplifying and collecting like terms, we get:
mABZ = 166 - 6.5x - 2mAA
We still need to find the measure of angle AAB, which we can do by using the equation for mA:
mA = 3x + 5
Since AABC is isosceles, we know that angle AAB is congruent to angle AAC, which means that mAAB = mAAC. Using the equation for mA, we can write:
mAAB = mAAC = 3x + 5
Now we can substitute this into the equation for mABZ:
mABZ = 166 - 6.5x - 2(mAAB)
Substituting mAAB, we get:
mABZ = 156 - 12.5x
Now we can solve for x by using the fact that mABZ + mZB + mzB + mz5 = 360 (since they form a quadrilateral). Substituting the expressions for mABZ, mZB, mzB, and mz5, we get:
156 - 12.5x + 5x - 9 + 1.5x + 17 = 360
Simplifying and solving for x, we get:
-5.5x = 196
x = -36
However, this value of x does not make sense since the measures of angles in a triangle and quadrilateral must be positive. Therefore, there is no solution that satisfies the given conditions and the answer is "no solution".