Question

two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio measure of their interior angles is 3:4 find the side of each polygon

Answer 1

Given :

Two polygon in which the ratio between their number of sides is 1:2

Ratio of interior angles is 3:4

To find :

Side of each polygon

Solution:

The interior angle of the polygon is given by,

( (x-2) /x ) * 180

Let us take the sides as a and 2a.

substituting in the above formula, we get

((a-2)/a ) *180 / ((2a-2)/2a ) *180  = 3/4

(a-2)/a   *  2/(a-1) = 3/4

(a-2) / (a-1) = 3/4

4a-8 = 3a-3

⇒ a=5

Therefore the sides are 5 and 10.

Answer 2

Given:

Ratio between the no. of sides=1:2

Ratio between measure of interior angles=3:4

Step-by-step explanation:

Let the no. of sides of the regular polygons be n and 2n. Then the interior angles would be:

(2n-4/n*90°) and (2(2n)-4/2n*90°)

It is given that the ratio between the measures of interior angles is 3:4.

Therefore:

2n-4/n*90°

_____________

2(2n)-4/2n*90° = 3/4

2n-4/n

_________

4n-4/2n. = 3/4

2n-4/n. • 2n/4n-4. =3/4

2(n-2)/1 • 2/4(n-1) =3/4

n-2

____

n-1. =3/4

4n-8=3n-3

4n-3n=-3+8

n=5

Therefore one polygon is of 5 sides and the other is of 10 sides.

Please solve it in the notebook to get a clear step by step answer.