Question

The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.

Answer 1

Step 1: Interiror angles, Exterior angles and Regular polygon

1. If all the sides and interior angles of the polygons are equal, they are known as regular polygons. The examples of regular polygons are square, rhombus, equilateral triangle, etc.
2. An angle formed inside the two adjacent sides of a polygon is known as interior angle.
3. An angle which is formed by one of the sides of any closed polygon and the extension of its adjacent side is known as exterior angle.

Step 2: Determine the number of sides of the polygon

The sum of interior angles of an regular polygon $=180°(n–2)$

The sum of exterior angles of an regular polygon $=360°$

$\begin{array}{rcl}180°(n–2)& =& 2\times 360°\\ (n–2)& =& 4\\ n& =& 6\end{array}$

Hence, the number of sides of the polygon is $6$.