Final answer:
To determine the number of sides of a regular polygon where each interior angle is 162°, we use the formula for the measure of an interior angle of a regular polygon. Solving for n we find that the polygon must have 20 sides, which doesn't match any of the options given, indicating a potential error in the question or options.
Step-by-step explanation:
The question is asking to determine the number of sides of a regular polygon given that each interior angle measures 162°. To solve this, we use the formula for the measure of each interior angle in a regular polygon, which is:
(n - 2) × 180° / n
Where n is the number of sides. We can set up the equation as follows:
162° = (n - 2) × 180° / n
Solving for n we get:
n - 2 = 162°n / 180°
0.9n - 2 = 162°n / 180°
162n = 180n - 360
18n = 360
n = 20
Since n must be an integer, we can see that the number of sides is 20, which is not listed among the provided options, indicating a possible error in the question or the options given.