The number of sides of two regular polygons is 5:4 and the difference between their angle is 90. Find the number of sides of the polygons.
Let the number of sides in the first polygon be 5x and the number of sides in the second polygon be 4x.
We know that angle of an n-sided regular polygon 
⇒ The angle of the first polygon 
⇒ The angle of the second polygon 
Thus,
⇒ 
∴ x = 2
Thus,
Number of sides in the first polygon = 5x = 10
Number of sides in the second polygon = 4x = 8
10