RBF3 wrote:I took an educated guess on this question but I was wondering why C was the answer?
Thanks for any help
Note that the measure of angle x depends upon the position of points Q, S and U only. Unless we don't know the fixed positions of these three points, we cannot uniquely determine the measure of angle x.
Statement 1: QR = RS
Thus position of Q and S is fixed. But U can be any point on PT and accordingly value of x will be different.
Not sufficient
Statement 2: ST = TU
Thus position of S and U is fixed. But Q can be any point on PR and accordingly value of x will be different.
Not sufficient
1 & 2 Together: Now the three points are fixed. Let's see whether we can find x. Refer to the image below.
On point S, the sum of the three angles must be equal to 180°.
Thus, (x + y + z) = 180° ..................................... (i)
angle PQS = (180° - angle RQS) = (180° - z)
angle PUS = (180° - angle TUS) = (180° - y)
Now in quadrilateral PQSU,
- Sum of all the internal angles = 360°
=> [x + 90° + (180° - y) + (180° - z)] = 360°
=> (x - y - z + 90°) = 0 .................................. (ii)
Now add (i) and (ii) => (2x + 90°) = 180° => x = 45°
Sufficient
The correct answer is C.
