Final answer:
The sum of the interior angles of a polygon is (n-2) * 180 degrees. By setting this equal to (9 * 360) and solving for n, we find that the polygon has 20 sides.
Step-by-step explanation:
To solve this problem, we need to use the fact that the sum of the interior angles of a polygon is equal to (n-2) * 180 degrees, where n is the number of sides of the polygon.
Let's assume the polygon has n sides. The sum of the interior angles of the polygon is (n-2) * 180. The sum of the exterior angles of the polygon is always 360 degrees, as the exterior angles of any polygon always add up to 360 degrees.
Given that the sum of the interior angles is 9 times the sum of the exterior angles, we can write the equation:
(n-2) * 180 = 9 * 360
Simplifying the equation, we have:
n - 2 = 9 * 2
n - 2 = 18
n = 20
Therefore, the polygon has 20 sides.