# Find the number of sides of each of the two polygons if the total number of sides of the polygons is 15 and the sum of the number of diagonals is 36

1
by Jbeatrice

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by Jbeatrice

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x + y = 15

First Polygon =

Second Polygon:

x + y = 15

Number of Diagonals in each polygon =

2

Where n = number of sides of regular polygon

Number of Diagonals for First Polygon, x:

=

2

Number of Diagonals for Second Polygon, 15-x:

=

2 2

Solve by factoring:

(x-9) (x-6) = 0

x - 9=0 x - 6 = 0

The two polygons have sides of 6 and 9:

Hexagon = 6 sides

Nonagon = 9 sides

To check:

The sum of sides of two polygons is 15

6 + 9 = 15

The diagonals:

Polygon with

2

=

2

= 18/2

=

Polygon with

2

=

2

= 54/2

=

The sum of the number of diagonals:

9 + 27 = 36