You're right that neither statement (1) nor (2) are sufficient, so I'll jump to what happens when we combine both pieces of information.
From (1) we can conclude that angleRQS = angleRSQ
From (2) we can conclude that angleTUS = angleTSU
We also know that:
(angleRQS + angleRSQ + angleR) + (angleTUS + angleTSU + angleT) = 360
Here's the big part: angleR + angleT = 90 (since they must add to angleP to get 180 degrees)
So, we can conclude that (angleRQS + angleRSQ) + (angleTUS + angleTSU) = 270
Since angleRQS = angleRSQ and angleTUS = angleTSU, we can say that: angleRSQ + angleTSU = 135
Finally, since angleRSQ + angleTSU + angle X must add to be 180, we can conclude that angle x is 45
So the answer is E
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angle rqs = angle rsq = y
2y = 180 - angle prt
y = 90 - angle prt /2
Similarly
angle sut = angle ust = z
z= 90 - angle stu
y + z = 180- x
90 + 90 - ( prt + stu )
180- 90 = 90
x = 90
Hence both are together sufficient
2y = 180 - angle prt
y = 90 - angle prt /2
Similarly
angle sut = angle ust = z
z= 90 - angle stu
y + z = 180- x
90 + 90 - ( prt + stu )
180- 90 = 90
x = 90
Hence both are together sufficient
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