Alana draws four squares, five pentagons and six octagons. marie draws n hexagons and notices that the combined number of diagonals in her hexagons is equal to the combined number of diagonals in alana’s polygons. what is the value of n?

The value of n is 17.

Step-by-step explanation:

We are given,

Alana draws 4 squares, 5 pentagons and 6 octagons.

Marie drew 'n' hexagons.

Also, the combined number of diagonals in Alana's polygons is equal to the combined number of diagonals in Marie's hexagons.

Since, the number of diagonals in a polygon is given by , where n is the number of sides.

So, using the formula, we have,

Number of diagonals in a square = 2

Number of diagonals in a pentagon = 5

Number of diagonals in a octagon = 20

Thus, total number of diagonals in Alana's polygons are 2×2 + 5×5 + 20×8 = 153.

Therefore, total number of diagonals in Marie's hexagons are 153.

As, number of diagonals in a hexagon = 9.

Total number of hexagons = = 17.

Hence, the value of n is 17.