Let's recall that If a set of 2 parallel lines, line m and line m, are crossed or cut by another line, line T, in our question, we say "a set of parallel lines are cut by a transversal.
Each of the parallel lines cut by the transversal has 4 angles surrounding the intersection.
These are matched in measure and position with a counterpart at the other parallel line.
At each of the parallel lines, there are two pairs of vertical angle. Each angle in the pair is congruent to the other angle in the pair.
In our question, the angle that measures 145 degrees is congruent with the opposites angles of angle x.
Let's recall that x and 145 degrees are adjacent supplementary angles. And these angles add up to 180 degrees. Then, for solve for x, we have:
x = 180 - 145
x = 35 degrees