Find the number of sides of each of the two polygons if the total number of sides of the polygons is 13, and the sum of the number of diagonals is 25.

1
by micogacho

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Find the number of sides of each of the two polygons if the total number of sides of the polygons is 13, and the sum of the number of diagonals is 25.

1
by micogacho

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x + y = 13

the formula for a diagonal in a polygon is

Also since the sum of the diagonals is 25 you can write:

Multiplying both sides by two you get,

Since you can transpose y to the other side you can get:

x + y = 13 can be written as: x = 13-y

Substituting,

Dividing by two you get,

(y-5)(y-8) = 0

Therefore the answer can be

1) x = 5, y = 8

OR

2) y=5, x=8