Geometry

Question Analysis:
This problem challenges students to determine when regular polygon interior angles first surpass a specified threshold, requiring:
Understanding of the interior angle formula
Inequality setup and solving
Interpretation of geometric constraints

Key Concept Explanation:
Fundamental principles involved:
Regular polygon interior angle formula: [(n - 2) × 180] / n
Inequality transformation techniques
Discrete nature of polygon sides (integer n ≥ 3)

Step-by-Step Solution:
Establish the inequality:
[(n - 2) × 180] / n > 175°
Multiply both sides by n:
(n − 2) × 180° > 175°n
Expand and simplify:
180°n − 360° > 175°n
5°n > 360°
n > 72
Conclusion: The smallest integer n satisfying this is 73.

Common Mistakes:
Stopping at...