Question

You are designing an amusement park ride with cars that will spin in a circle around a center axis, and the cars are located at the vertices of a regular polygon. The sum of the measures of the angles' vertices is 6120°. If each car holds a maximum of four people, what is the maximum number of people who can be on the ride at one time?

Answer 1

The answer is 144 people

Answer 2

To find the maximum number of people who can be on the ride at one time, we first need to determine the number of vertices (or cars) in the regular polygon.

The sum of the measures of the interior angles of a polygon can be found using the formula:

Sum of interior angles = (n - 2) × 180°

Where n is the number of vertices (or sides) of the polygon. In this case, the sum of the interior angles is 6120°. We can use this information to find the number of vertices:

6120° = (n - 2) × 180°

Now, let's solve for n:

6120° ÷ 180° = n - 2

34 = n - 2

n = 34 + 2

n = 36

So, there are 36 vertices in the polygon, which means there are 36 cars on the ride. Each car can hold a maximum of four people, so the maximum number of people who can be on the ride at one time is:

36 cars × 4 people/car = 144 people