CAT 2023 Slot 3 QA Question 19: n a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

Question

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

Accepted Answer

In a regular polygon, an interior angle and its corresponding exterior angle add up to $180^\circ$.

Let the exterior angle be e. Then the interior angle is $e + 120^\circ$.

$e + (e + 120^\circ) = 180^\circ$
$2e = 60^\circ$
$e = 30^\circ$

Number of sides is

$n = \dfrac{360^\circ}{30^\circ} = 12$