Final answer:
The sum of the interior angles of a convex pentagon is 540 degrees, while for a convex hexagon it is 720 degrees, confirming that the sum for a hexagon is greater than that for a pentagon.
Step-by-step explanation:
The statement that the sum of the interior angles of any convex pentagon will always be less than the sum of the interior angles of any convex hexagon is true. This is based on the formula for finding the sum S of the interior angles of a convex polygon with n sides, which is S = (n - 2) × 180 degrees. For a pentagon (5 sides), the sum is (5 - 2) × 180 = 540 degrees. For a hexagon (6 sides), the sum is (6 - 2) × 180 = 720 degrees. Therefore, the sum for a hexagon is indeed greater than that of a pentagon.