If one of the interior angles of a regular polygon is times of one of the interior angles of a regular decagon, then find the number of diagonals of the polygon.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 20
Given that
If one of the interior angles of a regular polygon is times of one of the interior angles of a regular decagon
As we know that
The interior angle of a regular polygon = (n - 2) × 180/n
where n is the side of the polygon
According to the question
⇒ (n - 2) × 180/n = (15/16) × (10 - 2) × 180/10
⇒ (n - 2) × 180/n = 135
⇒ (n - 2) × 4 = 3n
⇒ n = 8
Now, as we know the number of diagonals of the polygon = n × (n - 3)/2
= 8 × (8 - 3)/2 = 20