The only false answer is "The complement of X"
Let's look at each alternative.
"The supplement of S": the supplement of an angle is what it's lacking to 180° (e.g. the supplement of 30° would be 150°). Since S + T creates an angle that starts and ends on the same line (the one which crosses line a and line b), (S+T) is an 180° angle (given that both aren't 0°). So T is the supplement of S and is, obviously, equal to T.
"The complement of X": the complement of an angle is what it's lacking to 90°. You can clearly see that X is an acute angle, smaller than 90°, and that T is an obtuse angle, bigger than 90°; it is, therefore, clear that what X lacks to get to 90° can't be equal to T, which is itself bigger than 90°.
"The angle adjacent to Z": both W and Y are adjacent to Z since they share a side, have the same vertex and do not overlap. Since a and b are parallel and there is a LINE crossing them, which means that it doesn't change direction, you know that X = S and T = Y.
"The angle corresponding to R": I guess you can figure this one by now. :)