Question

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

Answer 1

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=12xy=12 solving for y: y=2xy=2x

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

I=(n−2)180nI=(n−2)180n

(x−2)180x(y−2)180y=34(x−2)180x(y−2)180y=34

Simplifying:

y(x−2)x(y−2)=34y(x−2)x(y−2)=34

Substituting for y:

2x(x−2)x(2x−2)=342x(x−2)x(2x−2)=34

Cross multiplying and distributing:

8x2−16x=6x2−6x8x2−16x=6x2−6x

Combine like terms:

2x2−10x=02x2−10x=0

Factor:

2x(x−5)=02x(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

Answer 2

$\rule{300}{2}$

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R:-}}}}$

See this attachment

This is the best possible answer

$\large{\boxed{\mathbf\pink{\fcolorbox{red}{yellow}{Hope\:you\:have}}}}$

$\large{\boxed{\mathbf\pink{\fcolorbox{red}{yellow}{Understood}}}}$

$<marquee>♥️Please mark it as♥️</marquee>$

$\huge\underline\mathcal\red{Brainliest}$

$</p><p>\huge{\boxed{\mathbb\green{\fcolorbox{red}{blue}{Thank\:You}}}}$

$\rule{300}{2}$