How many diagonals does a hexagon have?

Introduction / Context:
The number of diagonals of an n-gon equals the number of line segments between pairs of distinct vertices that are not sides.

Given Data / Assumptions:

• n = 6 (hexagon), vertices in general position.

Concept / Approach:
Total segments between vertex pairs = C(n,2). Subtract the sides, which are n in number. Thus diagonals = C(n,2) − n = n(n−1)/2 − n = n(n−3)/2.

Step-by-Step Solution:
Diagonals = 6*(6−3)/2 = 6*3/2 = 9.

Verification / Alternative check:
List vertices and count non-adjacent pairs; you will find 9 unique diagonals.

Why Other Options Are Wrong:
12 counts all segments to non-adjacent and adjacent; 10 and 6 are misapplications of the formula.

Common Pitfalls:
Forgetting to subtract the 6 sides from C(6,2) = 15; 15 − 6 = 9.

Final Answer:
9