Question

The number of sides of two regular polygons are in the ratio 5:4 and the difference between their interior angles is 6 degree. Find the number of sides in the two polygon​

Answer 1

Step-by-step explanation:

Let n be the Greatest Common Divisor (GCD) of the numbers under the question.

Then one polygon has 5n sides, while the other has 4n sides.

It is well known fact that the sum of exterior angles of each (convex) polygon is 360o.

So, the exterior angle of the regular 5n-sided polygon is 5n360o.

Similarly, the exterior angle of the regular 4n-sided polygon is 4n360o.

The difference between the corresponding exterior angles is 9o.

⇒  4n360o−5n360o=9o

⇒  4n1−5n1=360o9o

⇒  20n25n−4n=401

⇒  20n2n=401

⇒  n1=21

∴  n=2

⇒  Number of sides =4n=2×4=8 and 5n=2×5=10.

Note:

• 9o is nothing but 9 degree..

Hope this might help you...