Question

The ratio of the number of the sides of two regular polygon is 1:2,and the ratio of the sum of their interior angle is 3:8 Find the number of sides in each polygon?

Answer 1

Answer:

Step-by-step explanation:

Since, the ratio of its internal to external angle is 7:2, you can say that

its internal angle = 7x and exterior angle = 2x.

Therefore,

7x + 2x = 180

=> x = 20

Exterior angle = 40 degrees

now (exterior angle) = 360/(no. of sides)

solving, you will get no. of sides = 9.

Answer 2

Answer:

Step-by-step explanation:

Let the no. of sides of the first polygon be x

Therefore, the no. of sides of the second polygon

Sum of interior angles is 180(n-2) where n is the number of sides

By problem ==>

180(x-2) / 180(2x-2) = 3/8

By cross - multiplying, we get ==>

8[180(x-2)] = 3[180(2x-2)]

1440x-2880 = 1080x-1080

1440x-1080x = -1080+2880

360x = 1800

x = 1800/360

Therefore, x = 5

                2x = 2(5) = 10