Question

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

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

Answer 1

The correct option is A $9$

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