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

Answer:

144 people.

Step-by-step explanation:

Let n be the vertices, where cars are located.

We have been given that the sum of the measures of the angles' vertices is 6120°.

Let us find the number of vertices using formula:

$\text{Sum of all interior angles of a polygon with n sides}=180(n-2)$.

Upon substituting the given sum of the measures of the angles in this formula we will get,

$6120=180(n-2)$

Using distributive property $a(b+c)=a*b+a*c$ we will get,

$6120=180n-360$

Adding 360 to both sides of our equation we will get,

$6120+360=180n-360+360$

$6480=180n$

Upon dividing both sides of our equation by 180 we will get,

$\frac{6480}{180}=\frac{180n}{180}$

$36=n$

As the cars are located on the vertices of regular polygon, so there will be 36 cars in the ride.

We are told that each car holds a maximum of 4 people, so the number of maximum people who can ride at one time will be equal to 4 times 36.

$\text{Maximum number of people who can be on the ride at one time}=4\times 36$

$\text{Maximum number of people who can be on the ride at one time}=144$

Therefore, the maximum number of people who can be on the ride at one time is 144 people.