Question

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides if the polygon.

Answer 1

Let number of sides of a regular polygon = n
$\therefore$ Each interior angle $=\frac{2n-4}{n}$ right angles
$\therefore$ Sum of all interior angles $=\frac{2n-4}{n}\times n$ right angles
=(2n-4) right angles
But sum of exterior angles = 4 right angles
$\therefore$ According to the condition,
$(2n-4)=3\times 4$ (in right angles)
$2n-4=12\Rightarrow 2n=12+4=16\therefore n=\frac{16}{2}=8$
$\therefore$ Number of sides of the polygon = 8.