Neither statement alone is sufficient to determine the value of x.
When we combine the two statements, here's an efficient way to determine whether we have sufficient information to determine the value of x:
1. Plug in values for all of the angle measurements, satisfying the constraints in the problem and the rules of geometry.
2. Determine the value of x.
3. Plug in different values for all of the angle measurements, again satisfying the constraints in the problem and the rules of geometry.
3. Determine the value of x.
If the value of x stays the same, we have sufficient information.
If the value of x changes, we have insufficient information.
Below are two sets of angle measurements that satisfy both the rules of geometry and the constraints in the two statements:
∠PRT + ∠PTR = 90 because triangle PRT is a right triangle.
Since QR=RS, ∠RQS = ∠RSQ.
Since ST=TU, ∠UST = ∠SUT.
Since the sum of angles that form a straight line is 180, x = 180 - ∠RQS - ∠UST.
In each case, x=45.
Thus, when the two statements are combined, we have sufficient information to determine the value of x.
The correct answer is
C.
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