Final answer:
To find the number of sides in a regular polygon with an interior angle of 160 degrees, we use the formula relating the number of sides and the measure of the interior angles. The correct calculation reveals that the regular polygon would have 9 sides; therefore, none of the provided answer choices are correct.
Step-by-step explanation:
To find the number of sides in a regular polygon where each interior angle is 160°, we use the formula (n - 2) × 180° = n × (interior angle), where n is the number of sides.
We can rearrange the formula to solve for n as follows:
n × 160° = (n - 2) × 180°
160n = 180n - 360°
20n = 360°
n = 18
However, since 18 is not one of the answer choices, we need to check our work.
Let's review the formula for finding the measure of an interior angle of a regular polygon:
Interior Angle = ° = °
Using this correct formula:
Interior Angle = °
(n - 2) × 180° = n × 160°
n = 9
Thus, none of the answer choices a) 6, b) 8, c) 10, or d) 12, are correct.