Determine the value of $a$. [asy] pair w=(0,4); pair x=(0,0); pair y=(4,0); pair z=y+7/sqrt(2)*(1,1); dot(w); dot(x); dot(y); dot(z); draw(w--x--y--z--w); draw(0.15*w--0.15*w+0.15*y--0.15*y) ; label("$W$",w, NNW); label("$X$",x, SW); label("$Y$",y, SE); label("$Z$",z, E); label("4",(w+x)/2,W); label("4",(x+y)/2,S); label("9",(w+z)/2,NNW); label("$a$",(y+z)/2,SE); label("$135^\circ$",y, NNW); [/asy]

a=7

Step-by-step explanation:

The image is rendered and attached below.

Triangle WXY is an Isosceles right triangle, since WX=XY.

First, we determine the length of WY using Pythagoras Theorem.

Since triangle WXY is Isosceles,

Therefore:

Triangle WYZ is a right triangle with WZ as the hypothenuse.

Applying Pythagoras Theorem

answer: i literally just answered this question but they want me to do it again

step-by-step explanation: