For a<b<c; x,y and z should be in ascending order.

I : x is the avg of y and z

Then there are 2 possibilities; x,y and z are equal (or) either of y or z is lesser then x (and the other angle greater)

For Eg: if x = 60;

You could have y=z= 60 (or) y =10; z = 110.

Hence we can say for sure a<b<c is not satisfied.

II : You dont have a relation between the 3 angles, 2y = z-x (therefore, z>x, but y could be lesser or more)

Hence A

a<b<c, so x<y<z ?
(1) x=(y+z)/2
x is the arithmetic mean of y and z, in other words x is between y and z.
the lenght of x is between (y-z) and (y+z), so SUFFICIENT

(2) y=(z-x)/2
this info is wrong because y could not be less then z-x, so INSUFFICIENT

My answer is A