Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: In the diagram below, lines $k$ and $\ell$ are parallel.  Find the measure of angle $x$ in degrees. [asy]
size(200);
import markers;
pair A = dir(-22)*(0,0);
pair B = dir(-22)*(4,0);
pair C = dir(-22)*(4,2);
pair D = dir(-22)*(0,2);
pair F = dir(-22)*(0,1.3);
pair G = dir(-22)*(4,1.3);
pair H = dir(-22)*(2,1);
pair I = dir(-22)*(1.35,1.3);

markangle(Label("$x$",Relative(0.5)),n=1,radius=11,I+B,I,(2*I-B));

pair X,Y;

X=A;
Y=B;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=A;
Y=C;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=C;
Y=B;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=B;
Y=D;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

X=G;
Y=F;
draw(1.3*X-.3*Y--1.3*Y-.3*X);

label("$\ell$",1.4*A-.4*B);
label("$k$",1.4*F-.4*G);

//label("$x$",H+(.4,-.15));
label("$30^\circ$",A+(1,-.1));
label("$90^\circ$",B+(.4,.1));
label("$30^\circ$",B+(-1,.7));
[/asy]
user