Question

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 _______​

Answer 1

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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.