If we join W and Y......then triangle WXY will be a 45-45-90 right triangle with WY as the hypotenuse =
4 sqrt (2) = sqrt (32)
And angle WYZ = 135 - 45 = 90.....so.....triangle WYZ will also be a right triangle.....with WY as one leg and WZ as the hypotenuse
So...ZY = sqrt ( WZ^2 - WY^2) = sqrt ( 9^2 - (sqrt(32))^2 ) = sqrt ( 81 - 32) = sqrt (49) = 7 = a