What is the sum of the interior angles of a hexagon?

To determine the sum of the interior angles of a hexagon, we can use the formula for the sum of the interior angles of any polygon, which is given by ( (n - 2) \times 180 ) degrees, where ( n ) is the number of sides in the polygon.

In the case of a hexagon, there are 6 sides. By substituting ( n = 6 ) into the formula, we have:

[ (6 - 2) \times 180 = 4 \times 180 = 720 \text{ degrees}. ]

Thus, the sum of the interior angles of a hexagon is 720 degrees.

This formula works because it takes into account that a polygon can be divided into triangles, and since each triangle has angles that add up to 180 degrees, the number of triangles formed in a polygon with ( n ) vertices is ( n - 2 ). This understanding of polygons and their properties, specifically triangles, underlies the reasoning behind the formula.