If each interior angle of a regular polygon is 
, then what is the sum of the number of its diagonals and the number of its sides?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 21
Interior angle == (900/7)°
⇒ (n − 2)/n × 180 = (900/7)
⇒ (n − 2) = 5n/7
⇒ 7n - 14 = 5n
⇒ n = 7 [No. of sides]
Hence,
No. of diagonals = [n(n − 3)]/2 = [(7 × 4)]/2 = 14
Hence,
Sum of the number of diagonals and number of sides = 14 + 7 = 21