How many sides are there in a polygon which has 20 diagonals?
- A. 6
- B. 7
- C. 8 ✓
- D. 10
Correct Answer: C. 8
Explanation
The number of diagonals of an n-sided polygon is given by \frac{n(n-3)}{2}. Setting this equal to 20 gives n^2 - 3n - 40 = 0, which factors as (n-8)(n+5)=0. Since n must be positive, n = 8.
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