Question -
Answer -
Let the number of sides in the firstpolygon be 5x and
The number of sidesin the second polygon be 4x.
We know that, angleof an n-sided regular polygon = [(n-2)/n] π radian
The angle of thefirst polygon = [(5x-2)/5x] 180o
The angle of thesecond polygon = [(4x-1)/4x] 180o
Thus,
[(5x-2)/5x]180o – [(4x-1)/4x] 180o = 9
180o [(4(5x-2) – 5(4x-2))/20x] =9
Uponcross-multiplication we get,
(20x – 8 – 20x +10)/20x = 9/180
2/20x = 1/20
2/x = 1
x = 2
∴Numberof sides in the first polygon = 5x = 5(2) = 10
Number of sides inthe second polygon = 4x = 4(2) = 8