Question -
Answer -
Let the number of sides in the firstpolygon be 2x and
The number of sidesin the second polygon be x.
We know that, angleof an n-sided regular polygon = [(n-2)/n] π radian
The angle of thefirst polygon = [(2x-2)/2x] π = [(x-1)/x] π radian
The angle of thesecond polygon = [(x-2)/x] π radian
Thus,
[(x-1)/x] π/ [(x-2)/x] π = 3/2
(x-1)/(x-2) = 3/2
Uponcross-multiplication we get,
2x – 2 = 3x – 6
3x-2x = 6-2
x = 4
∴Number of sides in the first polygon = 2x = 2(4) = 8
Number of sides inthe second polygon = x = 4