The Ferris wheel has the shape of a regular n-gon (regular polygon with n vertices).
check the pictures attached to verify the following rule: the diagonals of a vertex divide a n-gon into (n-2) triangles.
This means that the sum of the measures of the interior angles of a n-gon is 180°(the sum of the measures of the interior angles of a triangle ) * (n-2), which is the total number of triangles constructed this way.
In a regular polygon, this total sum, is equally 'distributed' to each of the n vertices.
Conclusion:
the sum of the measures of a regular n-gon is 180(n-2)
the measure of 1 angle of a regular n-gon is [tex] \frac{180(n-2)}{n} [/tex]
In our problem, the sum of the measures of the interior angles is 7740º. So to find n, the number of vertices of the polygon:
7740º=180(n-2)
n-2=7740°/180°=43
n=45
So the Ferris wheel has 45 vertices, so 45 cars, each of which can hold 5 people.
Maximum number the Ferris can hold is 45*5=225 people
