CAT 2023 Geometry & Mensuration Question (Hard)

Question

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

Accepted Answer

Step 1 Let the exterior angle be x degrees. Then the interior angle is 120 x 120 degrees. Step 2 Since interior angle exterior angle 180 , we have 120 180 x x 120 180 2 120 180 2x 120 180 2 60 30 2x 60 x 30 Step 3 The exterior angle of a regular polygon is 360 n 360 , where n is the number of sides.

CAT 2023

Quantitative

Geometry & Mensuration

Hard

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

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