Question

The interior angles of a regular polygon measure $120^{\circ }$ each. The number of diagonals of the polygon is

• A. $9$
• B. $15$
• C. $44$
• D. $35$

Answer 1

Answer: (A)

In our problem, first we need the sides of the polygon.
Fact: Each interior angle of polygon of $n$ sides
$=\frac{2n-4}{n}\times 90^{\circ }$
$\therefore 120^{\circ }=\frac{2n-4}{n}\times 90^{\circ }$
$\Rightarrow 6=n$
$\therefore$ Number of diagonals
$={}^n{C}_2-n=\frac{n(n-3)}{2}=\frac{6\times 3}{2}=9$