Discussion
A polygon has 27 diagonals. The number of sides in the polygon is:
Answer: C
The formula for the number of diagonals is \(\frac{n(n-3)}{2}\).
\(\frac{n(n-3)}{2} = 27\)
\(n(n-3) = 54\)
We need two numbers with a difference of 3 that multiply to 54. By inspection, 9 and 6 satisfy this condition (9 × 6 = 54). Therefore, n=9. The polygon is a nonagon.
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