What are the definitions of regular and irregular polygons, a pentagon, and how to find the value of x in a quadrilateral?

$$
38^\circ + x^\circ + 2x^\circ + 82^\circ = 360^\circ
$$

$$
(38^\circ + 82^\circ) + (x^\circ + 2x^\circ) = 360^\circ
$$
$$
120^\circ + 3x^\circ = 360^\circ
$$

$$
3x^\circ = 360^\circ - 120^\circ
$$
$$
3x^\circ = 240^\circ
$$
$$
x^\circ = \frac{240^\circ}{3}
$$
$$
x^\circ = 80^\circ
$$
The correct option is (c).  
The value of $x^\circ$ is $\boxed{\text{80}^\circ}$.

Given: $V = 270\text{m}^3$, length ($l$) $= 9\text{m}$, breadth ($b$) $= 5\text{m}$.
$$
270\text{m}^3 = 9\text{m} \times 5\text{m} \times \text{height}
$$

$$
270\text{m}^3 = 45\text{m}^2 \times \text{height}
$$
$$
\text{height} = \frac{270\text{m}^3}{45\text{m}^2}
$$
$$
\text{height} = 6\text{m}
$$
The height of the cuboid is $\boxed{\text{6m}}$.

The sum of the interior angles of a polygon with $n$ sides is given by:
$$
\text{Sum} = (n-2) \times 180^\circ
$$

Given sum $= 198^\circ$.
$$
198^\circ = (n-2) \times 180^\circ
$$
$$
\frac{198^\circ}{180^\circ} = n-2
$$
$$
1.1 = n-2
$$
$$
n = 1.1 + 2
$$
$$
n = 3.1
$$
Since the number of sides of a polygon must be a whole number, a polygon with a sum of angles equal to $198^\circ$ does not exist. The smallest sum of angles for a polygon (a triangle) is $180^\circ$.

**b)** What is the value of t in the diagram?  
The diagram for this part of the question is missing from the image provided.