hello

It says, that the exterior angle of a polygon with m sides is equal to a regular polygon with g sides. So,

$\frac{360}{m} = \frac{180(g + 2)}{g}$

$360g = 180gm + 360m$

$2g = gm + 2m$

Factoring out g:

$2g - gm = 2m$

$g(2-m) = 2m$

So therefore, $g = \frac{2m}{2-m}$.

-24

Exterior angle of Mary's polygon =    360 / m

Interior angle of George's polygon  =   (g - 2)*180 / g

Since these are congruent....then

360 / m  =   (g - 2)  * 180 / g         cross - multiply

360g  =  180m * (g - 2)

360g = 180 gm - 360m

360m  = 180gm - 360g

2m = gm - 2g

2m =   g ( m - 2 )

g =  2m / ( m - 2)