BTGmoderatorDC wrote:
In the figure shown, what is the value of x?
(1) The length of line segment QR is equal to the length of line segment RS
(2) The length of line segment ST is equal to the length of line segment TU
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.
1. Plug in values for all of the angle measurements, satisfying the constraints in the problem and the rules of geometry.
2. Calculate 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. Calculate the value of x.
If the value of x is the SAME in each case, then we have sufficient information to determine the value of x.
If the value of x is NOT the same in each case, then we do NOT have insufficient information to determine the value of x.
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 that x=45.
The correct answer is
C.
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