Final answer:
The value of w is 16.
Step-by-step explanation:
The sum of the interior angles of a hexagon is given by the formula (n-2) * 180 degrees, where n is the number of sides of the polygon. In this case, n = 6. So, (6-2) * 180 = 4 * 180 = 720 degrees is the sum of the interior angles of a hexagon.
Since the hexagon is regular, all of its interior angles are congruent. Let's denote the measure of one angle as x°. Since there are 6 angles, we have 6x° = 720°. Dividing both sides of the equation by 6, we get x = 720/6 = 120°.
The given angle measure is (7w + 9)°. Setting it equal to 120°:
(7w + 9) = 120
7w = 120 - 9
7w = 111
w = 111/7 ≈ 15.857
Rounding to the nearest whole number, we get w = 16. Therefore, the value of w is 16.