Evaluate, (44-28)/(12 x -2) and 8² x -12 - 2496 / -12 x 9 without using mathematical tables or a calculator.

$$\frac{16}{24} = \frac{2 \times 8}{3 \times 8} = \frac{2}{3}$$

The value is $\boxed{\frac{2}{3}}$.

$$\frac{744}{72} = \frac{93 \times 8}{9 \times 8} = \frac{93}{9} = \frac{31 \times 3}{3 \times 3} = \frac{31}{3}$$

The value is $\boxed{\frac{31}{3}}$.

2. Use table of logarithms to evaluate: $\left(\frac{6.79 \times 0.391}{\log 5}\right)^{-\frac{3}{4}}$
Let the expression be $Y$. We need to find $\log Y$.

$$\log Y = -\frac{3}{4} \log \left(\frac{6.79 \times 0.391}{\log 5}\right)$$ $$\log Y = -\frac{3}{4} \left( \log(6.79 \times 0.391) - \log(\log 5) \right)$$ $$\log Y = -\frac{3}{4} \left( (\log 6.79 + \log 0.391) - \log(\log 5) \right)$$

Using 4-figure logarithm tables:
$\log 6.79 = 0.8319$
$\log 0.391 = \bar{1}.5922$
$\log 5 = 0.6990$

$$Y = \text{antilog}(\bar{1}.5653) \approx 0.3675$$

The value is $\boxed{0.3675}$.

3. Calculate the number of sides of the polygon.
Let $n$ be the number of sides of the polygon.
The sum of the interior angles of an $n$-sided polygon is given by the formula:

$$S = (n-2) \times 180^\circ$$

We are given that two interior angles are $178^\circ$ and $155^\circ$. The remaining $(n-2)$ angles each measure $143^\circ$.
So, the sum of the interior angles can also be expressed as:

$$S = 178^\circ + 155^\circ + (n-2) \times 143^\circ$$

$$180n - 360 = 333 + 143n - 286$$ $$180n - 360 = 143n + 47$$

$$180n - 143n = 47 + 360$$ $$37n = 407$$

$$n = \frac{407}{37}$$ $$n = 11$$

The number of sides of the polygon is $\boxed{11}$.