This is a GMATPrep question. There are several ways to solve, but if you can label an unknown angle with a letter in a question like this, and then use the basic angles facts to express every other angle in terms of that letter, you'll be able to answer any similar question, so that's the approach I'll use:
Statement 1 alone is not sufficient, because you can freely move point U around, and that changes the size of x. Similarly Statement 2 alone is not sufficient, because you can move point Q around and change x.
Using both Statements, say the angle at point R is y degrees. Then the angle at point T must be 90-y degrees, because in the big right triangle, the angles sum to 180.
Now Statement 1 tells us RQS is isosceles, so the angles at Q and S are equal. If the third angle in that triangle is y, then the two equal must sum to 180-y (because the sum of angles in a triangle is 180), so each angle is (180-y)/2 = 90 - (y/2)
Similarly, we know from Statement 2 that triangle TUS is isosceles. If the angle at T is 90-y degrees, the two equal angles must sum to 90+y degrees (because the sum of the three angles is 180). So each of the two equal angles is (90+y)/2 = 45 + (y/2)
Now we have labeled all three of the angles around point S -- they are 90 - (y/2), x, and 45 + (y/2). These angles form a straight line, so must add to 180. But notice what happens when we sum the three angles - the terms containing 'y' cancel out, and we get 135+x. So x must be 45 degrees, and the statements together are sufficient. The answer is C.
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