Question

each exterior angle of a regular polygon is two third of its interior angle find the number of sides in the regular polygon​



pls answer fast

Answer 1

Answer: 5 sides (Regular Pentagon)

Step-by-step explanation:

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

Answer 2

the answer is (8)

I had already salve it's 8