Given Angle D = x^ + 60^.

In a cyclic quadrilateral, opposite angles sum to $180^\circ$.
Angles D and B are opposite angles.
Given Angle D $= x^\circ + 60^\circ$.
Given Angle B $= x^\circ$.

Subtract 60 from both sides:

Divide by 2:

The value of $x$ is $\boxed{60}$.

We want to find $\text{log } 1080$.

Now, factorize 108:

So, $1080 = 2^2 \times 3^3 \times 10$.

Using the property $\text{log } (ab) = \text{log } a + \text{log } b$:

Using the property $\text{log } (a^n) = n \text{ log } a$:

We know that $\text{log } 10 = 1$ (assuming base 10 logarithm).

Given $\text{log } 2 = 0.30103$ and $\text{log } 3 = 0.47712$.

The value of $\text{log } 1080$ is $\boxed{3.03342}$.

The measurements are given to one decimal place