Question

the exterior angle of a regular polygon is one third of its interior angle .How many sides has the polygon?

Answer 1

we know that exterior angles of any polygons is 360 degree
then interior will be 360×3=1080
1080/90
=12 sides

Answer 2

Answer:

8 sides

Step-by-step explanation:

Let the interior angle of regular polygon be x

Since we are given that the exterior angle of a regular polygon is one third of its interior angle .

Exterior angle = $\frac{1}{3}x$

Since we know that the sum of interior angle and exterior angle is 180°

So, $x+\frac{1}{3}x=180$

$\frac{4}{3}x=180$

$x=180 \times \frac{3}{4}$

$x=135$

Formula : $180 \times \frac{n-2}{n}=\text{interior angle}$

$180 \times \frac{n-2}{n}=135$

$n=8$

Hence Polygon has 8 sides