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Angles and Diagonals of a Regular Polygon

CAT 2023 Slot 3 · Quantitative Ability · Easy · Geometry

This is an easy Quantitative Ability question from the CAT 2023 Slot 3 paper. It tests Geometry. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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

Answer

54

Explanation

Let II be the interior angle and EE be the exterior angle. We know I+E=180∘I + E = 180^\circ and I−E=120∘I - E = 120^\circ.

Subtracting gives: 2E=60∘  ⟹  E=30∘2E = 60^\circ \implies E = 30^\circ

Number of sides n=360∘E=360∘30∘=12n = \frac{360^\circ}{E} = \frac{360^\circ}{30^\circ} = 12.

Number of diagonals =n(n−3)2=12×92=54= \frac{n(n-3)}{2} = \frac{12 \times 9}{2} = 54.

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