The Polygon Interior Angle Sum Theorem states that the sum of the measures of the interior angles of a polygon can be calculated using the formula:
\[ S = (n - 2) \times 180^\circ \]
where \( S \) is the sum of the interior angles and \( n \) is the number of sides in the polygon.
For a hexagon, the number of sides \( n \) is 6. Plugging this value into the formula gives:
\[ S = (6 - 2) \times 180^\circ \] \[ S = 4 \times 180^\circ \] \[ S = 720^\circ \]
Therefore, the sum of the measures of the interior angles of the regular hexagon is \( \boxed{720^\circ} \).
3 answers