Question

Exterior angle of a regular polygon is two third of its interior. Find the number of sides

Answer 1

Let n be the number of the sides of the polygon.

Exterior Angle = 360degrees/n  -------- (i)

Interior angle = (n-2)*180/a          ---------(ii)


On solving(i),(ii) we get

= 2/3 (n-2)*180/n = 360/n

= 2(n-2)60 = 360

 n-2 = 360/120

          = 3

n = 3 + 2

    = 5



Hope this helps!

Answer 2

Exterior angle =two third of interior angle
Sum of exterior angle= two third of interior angle.
If sum of exterior angle is 'x'
Then sum of interior and=two third of x.
And we know sum of exterior angles of a regular polygon is 360°
Therefore
{2÷3}×x= 360°
Implies that
2x= (360×3)°
Implies that
2x=1080
Implies that
X= 540°
(2÷3)×x=360°
Let no. Of sides be n
We know (2n-4)*90°= sum of interior angles of the polygon
(2n-4)*90°=360°
180n-360°=360°
180n=(360+360)°
180n=720°
n=(720 ÷180)
=4( sides)