Given Angle D = x^ + 60^.

Step 1: Apply the property of cyclic quadrilaterals. 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 $= x^\circ$. $$ (x + 60) + x = 180 $$ Step 2: Solve the equation for $x$. $$ 2x + 60 = 180 $$ Subtract 60 from both sides: $$ 2x = 180 - 60 $$ $$ 2x = 120 $$ Divide by 2: $$ x = \frac{120}{2} $$ $$ x = 60 $$ The value of $x$ is $\boxed{60}$. Step 1: Express 1080 in terms of its prime factors and powers of 10. We want to find $\text{log } 1080$. $$ 1080 = 108 \times 10 $$ Now, factorize 108: $$ 108 = 2 \times 54 = 2 \times 2 \times 27 = 2^2 \times 3^3 $$ So, $1080 = 2^2 \times 3^3 \times 10$. Step 2: Apply logarithm properties. Using the property $\text{log } (ab) = \text{log } a + \text{log } b$: $$ \text{log } 1080 = \text{log } (2^2 \times 3^3 \times 10) $$ $$ \text{log } 1080 = \text{log } (2^2) + \text{log } (3^3) + \text{log } 10 $$ Using the property $\text{log } (a^n) = n \text{ log } a$: $$ \text{log } 1080 = 2 \text{ log } 2 + 3 \text{ log } 3 + \text{log } 10 $$ We know that $\text{log } 10 = 1$ (assuming base 10 logarithm). Step 3: Substitute the given values and calculate. Given $\text{log } 2 = 0.30103$ and $\text{log } 3 = 0.47712$. $$ \text{log } 1080 = 2(0.30103) + 3(0.47712) + 1 $$ $$ \text{log } 1080 = 0.60206 + 1.43136 + 1 $$ $$ \text{log } 1080 = 3.03342 $$ The value of $\text{log } 1080$ is $\boxed{3.03342}$. Step 1: Determine the absolute error for each measurement. The measurements are given to one decimal place