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Question

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.

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Solution

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 (2n4n) right angles.

Now,

According to the question

nm=545m4=n . . . (i)

Also,

(2n4n)90(2m4m) 90=9
(2n4)m(2m4)nmn=(110) . . . (ii)

From (i) and (ii), we get

(2×54m4)m(2m4)54m54m2=110 (10m16)(10m20)5m=110 4m=1mm=8

From (i)

n=54m=10

Thus,

n = 10, m = 8


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