Question

two regular polygon are such that the ratio between their number of sides is 1 ratio 3 and the ratio of the measures of their interior angles is 3 ratio 4. Find the number of sides of each polygon. ​

Answer 1

Answer:

Step-by-step explanation:

Question: Two regular polygons are such that the ratio between the number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. How would one find the number of sides of each polygon?

Let the number of sides of the regular polygon with the fewer number of sides be x, and y be the number of sides of the polygon with the greater number of sides.

xy=12 solving for y: y=2x

The measure of an interior angle of a regular polygon (I) is:

I=(n−2)180n

(x−2)180x(y−2)180y=34

Simplifying:

y(x−2)x(y−2)=34

Substituting for y:

2x(x−2)x(2x−2)=34

Cross multiplying and distributing:

8x2−16x=6x2−6x

Combine like terms:

2x2−10x=0

Factor:

2x(x−5)=0

Therefore, x = 0 or x = 5.

Eliminate x = 0, thus, x = 5 and y = 10, or the number of sides of the two regular polygons are 5 and 10