Question

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

Answer 1

Answer:

:5 sides (Regular Pentagon)

Let the interior angle be x

Then According to the question :

Exterior angle = (2/3)x

Now:Sum of interior and exterior angles = 180

Therefore: x+(2/3)x=180

                     (5/3)x=180

                  =>x=108

 Assume that the polygon has n sides then;

 Anglesum property=> Total interior angle= 108*n....................[1 ]

                        Also Total Interior angle = (n-2)*180.....................[2]

 Equating [1 ] and [2]

     108*n=(n-2)180

     Solving we get n=5

Therefore It is a 5 sided regular ploygon or a Pentagon