The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9∘. Find the number of sides of the polygons.
Let n and m be the number of sides in the two regular polygon respectively.
We know that each angle of n - sided regular polygon is (2n−4n) right angles.
According to the question
nm=54⇒5m4=n . . . (i)
⇒ (2n−4)m−(2m−4)nmn=(110)∘ . . . (ii)
From (i) and (ii), we get
(2×54m−4)m−(2m−4)54m54m2=110⇒ (10m−16)−(10m−20)5m=110⇒ 4m=1m⇒m=8
n = 10, m = 8