DS problem from Geometry

[s.pharmaco]

Well I have a problem where I am not able to understand the solution

The problem is: In the attached figure


In PQR , if PQ = QR, what is Z?
(1) x = 65 (2) y = 57

The answer is that both are rquired to answer the question, however i think only A is required because since PQ=QR z would be equal to angle QRP which is equal to y because of opposite angles. Since x is an external angle i.e. equal to z + angle QRP it will be equal to 2z. I i know value of x then I can calculate z. Can anyone please help why its answer is C and not A

[avinashrao9]

If QRP = y = z because of alternate angles, even PQR = x because of alternate angles.
Since it is an isoceles triangle,
According to (1), it is 2z + x = 180 => z = 57.5
According to (2), z = y = 57

Why not answer (D). Individual choices are SUFFICIENT.

[shatyasree]

D is correct since statement alone is sufficient

[Patrick_GMATFix]

Notice that since we're dealing with an isosceles triangle, the two angles at the bottom are the same. As a result, we only need to know 1 of the angles in the triangle to discover all three.

Rephrase: What is any one angle in the triangle?

Each statement gives you an angle in the triangle since vertical angles (angles that face each other across two intersecting lines) are always equal.

D is correct.