Final answer:
The interior angle of a regular polygon is 160 degrees. By using the sum of interior angles formula and algebra, it is determined that the polygon has 18 sides.
Step-by-step explanation:
The measure of the interior angle of a regular polygon is 160 degrees, so we can use this information to find out how many sides the polygon has. The formula for the sum of the interior angles (S) of a polygon with n sides is S = (n - 2) × 180 degrees. For a regular polygon, where all angles are equal, each interior angle (A) is given by A = S / n. We can combine these to get A = ((n - 2) × 180) / n. When the interior angle is 160 degrees, you can set up the equation 160 = ((n - 2) × 180) / n and solve for n.
To solve for n, you first multiply both sides by n which gives you 160n = (n - 2) × 180. Simplifying it leads to 160n = 180n - 360. By subtracting 160n from both sides, you are left with 360 = 20n, which when you divide by 20, gives you n = 18. Therefore, a regular polygon with an interior angle of 160 degrees has 18 sides.