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CAT 2023 Slot 3 QA Question & Solution

GeometryMedium

Question

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

Solution

The sum of the interior angles of a polygon of 'n' sides is given by $\left(2n-4\right)\times\ 90$, and the sum of the exterior angles of a polygon is 360 degrees.

So, the difference between them will be 120 * n

=> $\left(2n-4\right)90-360=120n$

=> 60n = 720 => n = 12.

We know that the number of diagonals of a regular polygon is nC2 - n = 12C2 - 12 = 66 - 12 = 54.