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vlabodo [156]
2 years ago
11

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?

Mathematics
1 answer:
Leokris [45]2 years ago
5 0
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 \frac{180(n-2)}{n}
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:
<span>
7740º=180(n-2)

n-2=7740</span>°/180°<span>=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</span>

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