+148 Mary draws an equiangular polygon with m sides, and George draws an equiangular polygon with g sides, where m is less than g. If the exterior angle of Mary's polygon is congruent to the interior angle of George's polygon, find g.
help, anyone???
+62 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
+129852 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)
