To find BZ, we need to use the Angle Bisector Theorem, which states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the other two sides.

Given that ∠ABC = 60° and BZ is the angle bisector, we can use the theorem to find the length of BZ.

Let's assume the length of AB = x and the length of BC = y.

Now, according to the Angle Bisector Theorem:

AB / AC = BZ / CZ

Since AC = AB + BC, we can write this as:

x / (x + y) = BZ / (BC - BZ)

Plug in the values:

x / (x + y) = BZ / (y - BZ)

Let's substitute x as BZ and simplify the equation:

BZ / (BZ + y) = BZ / (y - BZ)

Cross multiply to get rid of the denominators:

BZ(y - BZ) = BZ(BZ + y)

yBZ - BZ^2 = BZ^2 + yBZ

yBZ = 2BZ^2 + yBZ

yBZ - yBZ = 2BZ^2

0 = 2BZ^2

This gives us BZ = 0.

Therefore, BZ has a length of 0 units.