Question

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?

Answer 1

80

Explanation:

i took test

Answer 2

well, we know each car holds 5 folks, we know also that the "interior" angles of the wheel sum up to 7740º, so hmm how many cars on that "regular polygon" wheel anyway?

well
`\bf \textit{sum of all interior angles in a polygon}\\\\ s=180(n-2)\ \begin{cases} n=\textit{sides in the polygon}\\ ----------\\ s=7740 \end{cases}\implies 7740=180(n-2) \\\\\\ \cfrac{7740}{180}=n-2\implies 43=n-2\implies \boxed{45=n}`

so the ferris wheel has 45 sides, is a polygon of 45 sides... that means it has 45 cars, each car can hold 5 folks, so it can hold a maximum of 45 *5