In rectangle KLMN, KM = 8x+20 and LN = 60. Find the value of x.

In a rectangle, opposite sides are congruent. Therefore, KM = LN.

We have the equation 8x + 20 = 60.
Subtracting 20 from both sides, we get 8x = 40.
Dividing both sides by 8, we get x = 5. Answer: \boxed{5}.