The number of sides of two regular polygons is 5:4 and the difference

1.	The number of sides of two regular polygons is 5:4 and the difference between their angles is 9°. Find the number of sides of the polygons.
Answer» Suppose the number of sides in the first polygon be 5x and The number of sides in the second polygon be 4x. As we know that, angle of an n-sided regular polygon = [(n - 2)/n]π radian The angle of the first polygon = [(5x - 2)/5x]180^° The angle of the second polygon = [(4x - 1)/4x]180^° Hence, [(5x - 2)/5x]180^° – [(4x - 1)/4x]180^° = 9 180^°[(4(5x - 2) – 5(4x - 2))/20x] = 9 Now, upon cross-multiplication we get, (20x – 8 – 20x + 10)/20x = 9/180 2/20x = 1/20 2/x = 1 x = 2 ∴Number of sides in the first polygon = 5x = 5(2) = 10 Thus, the number of sides in the second polygon = 4x = 4(2) = 8

The number of sides of two regular polygons is 5:4 and the difference between their angles is 9°. Find the number of sides of the polygons.

Answer»

Suppose the number of sides in the first polygon be 5x and

The number of sides in the second polygon be 4x.

As we know that, angle of an n-sided regular polygon = [(n - 2)/n]π radian

The angle of the first polygon = [(5x - 2)/5x]180^°

The angle of the second polygon = [(4x - 1)/4x]180^°

Hence,

[(5x - 2)/5x]180^° – [(4x - 1)/4x]180^° = 9

180^°[(4(5x - 2) – 5(4x - 2))/20x] = 9

Now, upon cross-multiplication we get,

(20x – 8 – 20x + 10)/20x = 9/180

2/20x = 1/20

2/x = 1

x = 2

∴Number of sides in the first polygon = 5x = 5(2) = 10

Thus, the number of sides in the second polygon = 4x = 4(2) = 8