CAT 2023 Slot 3 QA Q19 Geometry

Question 19 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

TITA: type in the answer. There are no options and no negative marking.

Answer: 54 Geometry TITA

Solution

  1. \(I-E=120^\circ\) and \(I+E=180^\circ\), so \(E=30^\circ\) and \(n = \frac{360}{30}=12\).
  2. Diagonals \(= \frac{n(n-3)}{2} = \frac{12\times9}{2} = 54\).

Same concept in other years

See every question on Regular polygons: exterior angle = 360°/n.

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