alex.gellatly wrote:In the figure attached, 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.
I guessed and got it right.. could someone please explain. THANKS
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 the angle measurements, satisfying the conditions in the problem and the rules of geometry.
2. Determine the value of x.
3. Plug in different values for all the angle measurements, still satisfying the conditions 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.
The image below shows two sets of angle measurements that satisfy both the rules of geometry and the information given 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 know that x=45 and that the two statements combined are sufficient.
The correct answer is
C.
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