first off, note that the conditions given in statements (1) and (2), individually, are identical. (i.e., if you flip the triangle around, statement 1 becomes statement 2, and vice versa.) that's a humble observation, but it serves to eliminate choices a and b in a hurry: if statement (1) is sufficient then statement (2) must be as well, and vice versa.

that leaves us with the last 3 choices.

you can visualize the fact that one of the two statements alone won't do the job:
imagine that statement (1) alone is true, making triangle QRS isosceles. that means segment QS is fixed in place.
however, there are no restrictions on triangle STU. that means, in effect, that we can move point U wherever we feel like moving it.
as we 'slide' point U along the bottom of the triangle, the value of x changes; therefore, statement (1) alone (and hence statement (2) alone) is insufficient.

if you don't buy the above argument, or if it's just something you'd never possibly think of within the time limit, then you could always try plugging in numbers and seeing that x can have different values.

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statements (1) and (2) together:
since the triangle is a right triangle, we know that angles R and T must add to 90 degrees. let angle R be y degrees, and let angle T be (90 - y) degrees.
then
each of angles RQS and RSQ is (180 - y)/2 = 90 - y/2 degrees; and
each of angles TSU and TUS is (180 - (90 - y))/2 = 45 + y/2 degrees.
therefore, since angle RSQ, x, and angle TSU make a straight line together,
x = 180 - RSQ - TSU
= 180 - (90 - y/2) - (45 + y/2)
= 45 degrees.
sufficient
answer = c