Geometry

Question Analysis:
This question compares two regular polygons and involves both ratio reasoning and interior angle formulas.
The main focus is on reverse-solving the number of sides, then comparing interior angles.

Key Concept Explanation:
Interior angle = [(n - 2) × 180] / n
We can find n from one polygon and then divide by 3 to find the smaller polygon.

Step-by-Step Solution:
Let the number of sides of the larger polygon be n.
We’re told the interior angle = 160°. Use the formula:
160 = [(n - 2) × 180] / n
Multiply both sides by n:
160n = 180n - 360
Subtract:
20n = 360 → n = 18
So the smaller polygon has: 18 ÷ 3 = ...