Geometry

Question Analysis:
You are given the interior angle of a regular polygon, and must determine the number of sides.
The main focus is on converting an angle measurement into a side count using exterior angle relationships.

Key Concept Explanation:
In any polygon:
 Interior + Exterior = 180°
For regular polygons:
 Exterior = 360 ÷ n
 So: n = 360 ÷ (180 – given interior angle)

Step-by-Step Solution:
Interior angle = 165°
Exterior = 180 – 165 = 15°
Number of sides = 360 ÷ 15 = 24

Common Mistakes:
Using wrong formula like (n – 2) × 180