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The question is from the topic polygons. It discusses about the angles formed by diagnols in a polygon.CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 45: The number of sides in a regular polygon is ‘T’ times the number of diagonals in it. What is the interior angle of this polygon in terms of T?

  1. 180 * \\frac{(T+2)}{(3T+2)}\\)
  2. 540 * \\frac{(T+2)}{(3T+2)}\\)
  3. 360 * \\frac{(T+2)}{(3T+2)}\\)
  4. 90 * \\frac{(T+2)}{(3T+2)}\\)

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Explanatory Answer

Method of solving this CAT Question from polygons: Knowing the relationship between number of sides and diagonals of a polygon would be useful.

Let the number of sides in the regular polygon be n.
Therefore, Number of diagonals = nC2 - n = \\frac{n(n-1)}{2}\\) - n = \\frac{n^2-3n}{2}\\)
Given, Number of sides = p x Number of diagonals
=> n = T * \\frac{n^2-3n}{2}\\)
=> n = \\frac{2}{T}\\) + 3
Interior angle = (n-2) * \\frac{180}{n}\\) + 3
= (\\frac{2}{T}\\)+ 3 - 2) * \\frac{180}{2/T + 3}\\)
= (\\frac{2}{T}\\) + 1) * \\frac{180}{2/T + 3}\\)
= 180 * \\frac{(T+2)}{(3T+2)}\\)

The question is " What is the interior angle of this polygon in terms of T?"

Hence, the answer is 180 * \\frac{(T+2)}{(3T+2)}\\)

Choice A is the correct answer.


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