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

Since KL and MN are opposite sides of a rectangle, they must be equal in length.

So, we have:
KM = LN
8x + 20 = 52
8x = 52 - 20
8x = 32
x = 32/8
x = 4

Therefore, the value of x is 4.