The car at each vertex of a ferris wheel holds a maximum of 5 people. the sum of the measures of the angles of the ferris wheel is 7740º. what is the maximum number of people that the ferris wheel can hold?

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 
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