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the number of sides is 30

i was able to get the number of sides but i don't know how to show the solution

the number of side is 9 and 6
i just need a solution how to get this

then the numbers of sides of the polygon should be polygons

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http://www.dummies.com/how-to/content/how-to-find-the-number-of-diagonals-in-a-polygon.html

So the number of diagonals of a polygon with \(n\) sides is \(\dfrac{n(n-3)}2\)

Why don't you set up equations :)

number of diagonals i already given. i need a solution.

can you help me?

You could try letting the numbers of sides of the two polygons be \(m\) and \(n\) respectively :)

can you pls show me the solution. i got this m(m-3)/2 + n(n-3)/2 = 36

ok here's a hint: \(m=15-n\)

substitute 15-n for m

huh?

substitute \(m=15-n\) to \(\dfrac{m(m-3)}2+\dfrac{n(n-3)}2=36\) :)

into*

\[\left( 15-n ^{} \right)^{2}-3\left( 15-n \right)+n ^{2}-3n=72\]

yep, and this will be a quadratic :)

im stuck

i got -108 = -27n+n^2

Have you learnt quadratic? :)

Use quadratics pl0x

can you just pls provide me the whole solution
im stuck. sorry if im stupid about this..

i stop studying for 5years and i need to recall everything about geometry

2n^2-30n+108=0

(_n+_)(_n-_) factor

you did it right you just got 27 instead of 30

how did you get the 30?

got it

from the first equation
225-30n+n^2-45+3n+n^2-3n=72

combine like terms

after that. what is next?

(15-n)^2 gave me the thirty

how do i get the n now?

then you factor the 2n^2-30n+108
you can divide both sides by two to make it easier
n^2-15n+54

two factors of 54 that total to -15

(x-_)*(x-_)=0

(n-9)(n-6)

yes
so those are your sides

thank you so much for your patience with me. i really appreciate it.