In rectangle KLMN, KM = 8x+20 and LN = 52. Find the value of x.

Since KLMN is a rectangle, KM = LN.

So, 8x + 20 = 52.
Now, let's solve this equation for x.
8x + 20 = 52
Subtracting 20 from both sides, we get:
8x = 32
Now, dividing both sides by 8, we get:
x = 4
Therefore, the value of x is 4.