Geometry

Question Analysis:
This algebra-based question requires understanding the relationship between interior and exterior angles in regular polygons and solving for integer solutions.

Key Concept Explanation:
Fundamental Relationship: For any regular polygon:
Interior angle + Exterior angle = 180°
Number of sides (n) = 360° ÷ Exterior angle
Integer Solution Requirement: The calculated number of sides must be a whole number.

Step-by-Step Solution:
Set Up the Equation:
Interior angle+Exterior angle = 180°
6x + 3x = 180°
9x = 180°
x = 20°
Calculate Exterior Angle: Exterior...