CAT 2023 Slot 3 Solved Paper

The sum of the interior angles of a polygon of ' $\mathit{n}$ ' sides is given by $\left(2\mathit{n}-4\right)\times 90$, and the sum of the exterior angles of a polygon is 360 degrees.
So, the difference between them will be $120*\mathrm{n}$
$\Rightarrow \left(2\mathit{n}-4\right)90-360=120\mathit{n}$
$\Rightarrow 60\mathit{n}=720\Rightarrow \mathit{n}=12$
We know that the number of diagonals of a regular polygon is $\mathrm{nC}2\mathrm{n}=12\mathrm{C}2-12=66-12=54$.