The ratio of the exterior angles of two regular polygons is 3 : 2 and the ratio of their interior angles is 3:4 then, the total number of sides of both the polygons is _______
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Sum of interior angles regular polygons = (n−2)×180
sides of two regular polygons= x and y
So, x/y=3/4
x=3y/4
Sum of interior angles regular polygons (x)=(x−2)×180
Sum of interior angles regular polygons (y)=(y−2)×180
(x−2)×180/(y−2)×180=2/3
x−2/y−2=2/3
3y/4−2/y−2=2/3
3y−8/y−2=8/3
9y−24=8y−16
y=8
x=3y/4=3×8/4=6
Answer (1) 6 and 8, (2) 8 and 6.
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