The sum of the interior angles in a hexagon is $720$ degrees.

To grasp why this is true, we can utilize a formula applicable to any polygon. The formula for calculating the sum of the interior angles of a polygon is given by

where $n$ represents the number of sides in the polygon. In the case of a hexagon, which has $6$ sides, we substitute $n$ with $6$. This results in:

When we multiply $4$ by $180$, we find that the sum of the interior angles is $720$ degrees.

Another way to visualize this concept is by dividing the hexagon into triangles. By drawing all the diagonals from a single vertex of the hexagon, you can see that it can be split into $4$ triangles. Since each triangle has interior angles that sum to $180$ degrees, and there are $4$ triangles, the total sum of the interior angles in the hexagon can be calculated as:

This approach is not limited to hexagons; it works for any polygon. For instance, a pentagon, which has $5$ sides, would have a sum of interior angles calculated as follows:

Understanding this formula enables you to quickly determine the sum of the interior angles for any polygon, making it an invaluable tool in your mathematical toolkit.