Given that the hexagon is a regular hexagon, this means that all the side length are congruent and all internal angles are congruent. The question requires us to solve for the measure of an internal angle. Given the aforementioned definition of a regular polygon, this means that there must only be one correct answer.

In order to solve for the answer, the question provides additional information that isn't necessarily required. The measure of an internal angle can be solved for using the equation:

\(\displaystyle \frac{180^{\circ}(n-2)}{n}\) where \(\displaystyle n\) is the number of sides of the polygon.

In this case, \(\displaystyle n = 6\).

For this problem, the information about the side length may be negated.

\(\displaystyle \frac{180^{\circ}(6-2)}{6}\)

\(\displaystyle \frac{180^{\circ}(4)}{6}\)

\(\displaystyle \frac{180^{\circ}(2)}{3}\)

\(\displaystyle 120^{\circ}\)

The area has no relevance to find the angle of a regular hexagon.

There are 6 sides in a regular hexagon.  Use the following formula to determine the interior angle.

\(\displaystyle \theta=(n-2)\cdot 180\)

Substitute \(\displaystyle n=6\) sides to determine the sum of all interior angles of the hexagon in degrees.

\(\displaystyle \sum\theta=(6-2)\cdot 180=720\)

Since there are 6 sides, divide this number by 6 to determine the value of each interior angle.

\(\displaystyle \frac{720}{6}=120\)

Below is regular Hexagon \(\displaystyle HEXAGO\) with center \(\displaystyle C\), a segment drawn from \(\displaystyle C\) to each vertex - that is, each of its radii drawn.

Each angle of a regular hexagon measures \(\displaystyle 120^{\circ }\); by symmetry, each radius bisects an angle of the hexagon, so 

\(\displaystyle m \angle CAG = 60 ^{\circ }\).

The angles of a rectangle must measure \(\displaystyle 90^{\circ }\), so it has been disproved that Quadrilateral \(\displaystyle CAGO\) is a rectangle.

Suppose Hexagon \(\displaystyle HEXAGO\) is regular. Each angle of a regular polygon of \(\displaystyle N\) sides has measure

\(\displaystyle \frac{(N-2)180^{\circ }}{N}\)

A hexagon has 6 sides, so set \(\displaystyle N = 6\); each angle of the regular hexagon has measure  

\(\displaystyle \frac{(6-2)180^{\circ }}{6} = \frac{ 4 \cdot 180^{\circ }}{6} = 120^{\circ }\)

Since one angle is given to be of measure \(\displaystyle 108 ^{\circ }\), the hexagon cannot be regular.

The sum of the exterior angles of any polygon, one at each vertex, is \(\displaystyle 360^{\circ }\). In a regular polygon, the exterior angles all have the same measure, so divide 360 by the number of angles, which, here, is 20, the same as the number of sides.

\(\displaystyle 360\div 20 = 18\) 

The sum of the interior angle measures of a hexagon is \(\displaystyle 180 (6-2)=720^{\circ }\)

Add the angle measures in each group.

\(\displaystyle 120+120+120+120+120+120=720\)

\(\displaystyle 95+105+115+125+135+145=720\)

\(\displaystyle 110+110+110+110+110+170=720\)

\(\displaystyle 118+119+120+120+121+122=720\)

In each case, the angle measures add up to 720, so the answer is that all of these can be the six interior angle measures of a hexagon.