Geometry

Question Analysis:
This problem tests:
Inequality interpretation
Algebraic manipulation with polygon angles
Integer solution determination

Key Concept Explanation:
Relevant mathematical concepts:
Regular polygon interior angle formula
Solving compound inequalities
Integer constraints in geometric problems

Step-by-Step Solution:
Set up inequality:
140° < (n - 2) × 180°/n < 160°
Solve left inequality:
140°n < 180°n - 360°
-40°n < -360° → n > 9
Solve right inequality:
180°n - 360° < 160°n
20°n < 360° → n < 18
Integer solutions:
n = 10, 11, 12, 13, 14, 15, 16, 17 → 8 values

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