The measures of 2 vertical angles are always equal, so we have:
7x+182=9x+192.
Rearranging, we have 182-192=9x-7x, which simplifies to -12=2x.
Thus, x=-6.
This means that the angles are:
i) 7x+182=7(-6)+182=182-42= 140(degrees).
ii) 9x+194=9(-6)+194=194-54=140 (degrees, as expected.)
Answer: x=-6