If the measure of each interior angle of a regular polygon is 513/7ᵒ , then the ratio of the no. of its diagonals to the number of its sides is:

If the measure of each interior angle of a regular polygon…

If the measure of each interior angle of a regular polygon is $51\frac{3}{7}^o$ , then the ratio of the no. of its diagonals to the number of its sides is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 2 : 1.

Exterior angle of a regular polygon = 360°/n

(n = number of sides of polygon)

Then,

$51\frac{3}{7}^o$ = 360°/n

⇒ 360/7 = 360/n

⇒ n = 7

No. of diagonals =

Hence,

Ratio of the no. of its diagonals to the number of sides = 14 : 7 = 2 : 1

SSC CGL 2019 PYQ — Question 15