Question 19.
In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
A
B
C
D
Question Explanation
Text ExplanationVideo Explanation
The sum of the interior angles of a polygon of 'n' sides is given by (2n−4)× 90, and the sum of the exterior angles of a polygon is 360 degrees.
So, the difference between them will be 120 * n
=> (2n−4)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.
