We know that the sum of the angles in triangle MLK is 180 degrees. Therefore, we can find the measure of angle KLM as follows:
m∠MLK + m∠KLM + m∠LMK = 180
130 + m∠KLM + m∠LMZ = 180
We also know that angles ZLK and MLZ are vertical angles, so they are congruent. Therefore:
m∠ZLK = m∠MLZ
x + 86 = x + 66
86 = 66
This is a contradiction, so there is no value of x that satisfies the given conditions. Therefore, we cannot find the measure of angle ZLK.