The total number of sides in two regular polygons is 13, and total number of diagonals is 25. how many sides are in each polygon? PLS ANSWER QUICK!

Answer 1

The total number of sides in two regular polygons is 13, and total number of diagonals is 25. how many sides are in each polygon?

Answer 2

let x be the sides of one polygon
y be the sides of the other polygon

x + y = 13
y = 13 - x

then the formula for the number of polygons is n(n - 3) / 2

x(x - 3) / 2 + y(y - 3) / 2 = 25
x(x - 3) / 2 + ( 13 - x) ( 13 - x - 3) / 2 = 25
x( x - 3 ) / 2 + ( 13 - x) ( 10 - x) / 2 = 25

solve for x
x = 8
y = 13 - 8 = 5

I dunno

Answer 3

Number of sides of first polygon : x
number of sides in the 2nd = 13-x

number of diagonals of an n-gon = C(n,2) - n = n(n-1)/2 - n
(I subtracted n because the n sides are not diagonals)

number of diagonals for the x-gon
= C(x,2) - x = x(x-1)/2 - x
number of diagonals or the other
= C(13-x, 2) - (13-x) = (13-x)(12-x)/2 - 13 + x

(13-x)(12-x)/2 - 13 + x + x(x-1)/2 - x = 25
multiply and expand at the same time
156 - 25x + x^2 - 26 + 2x + x^2 - x - 2x = 50
2x^2 - 26x + 80 = 0
x^2 - 13x + 40 = 0
(x-5)(x-8) = 0
x = 5 or x = 8

Symmetric solution, that is,
if x = 5, 13-5 = 8
if x = 8, 13-8 = 5

So one is a pentagon, the other an octagon.