Question

If the sum of the interior angles of a regular polygon is ${1440}^{\circ }$, then the polygon must be a.

• A. heptagon
• B. octagon
• C. decagon

Answer 1

The correct option is C decagon

Given, Sum of the interior angles of a regular polygon $={1440}^{\circ }$
As we know, sum of internal angles of n-sided polygon$=(n-2){180}^{\circ }$
$\Rightarrow$ $(n-2){180}^{\circ }$ $={1440}^{\circ }$
$\Rightarrow$ $(n-2)$ $=\frac{1440}{180}=8$
$\Rightarrow$ $n=10$
Since, 10 sided polygon is know as decagon
$\therefore$ The polygon must be a decagon.