kwah wrote:I have attached a question from GMATPrep Test.

Answer: C

I got the right answer however, would appreciate if someone can explain steps to figure out the answer.

I understand that 1) and 2) are telling us the triangles are equilateral. However, how does this give us 'x' degrees?

Help is appreciated,
K

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.

Combining (1) and (2), 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° ...Equation 1

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 ...Equation 2

Adding equations 1 and 2, we get (2x + 90°) = 180° => x = 45°; SUFFICIENT.

The correct answer is C.