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NDA 1 2025 Maths, question 17

Topic: Algebra

Q17

How many sides are there in a polygon which has 20 diagonals?

  1. (a) 6
  2. (b) 7
  3. (c) 8Correct answer
  4. (d) 10

Solution.

Answer: (c) 8

  1. An nn-sided polygon has n(n−3)/2n(n - 3)/2 diagonals.
  2. Therefore n(n−3)/2=20n(n - 3)/2 = 20, or n2−3n−40=(n−8)(n+5)=0n^{2} - 3n - 40 = (n - 8)(n + 5) = 0.
  3. A side count must be positive, so n=8n = 8.