Question

A carousel has 30 cars. Determine the angle of rotation that maps #6 to car #19.

Answer 1

Answer:  The answer is 260°.

Step-by-step explanation: Given that a Carousel has 30 cars. We need to find the angle of rotation which maps car no. 6 to car no. 19.

Now, the Carousel will make a regular polygon with 30 sides and each car as a vertex.

So, angle of symmetry for the polygon is

$\theta=\dfrac{360^\circ}{30}=20^\circ.$

Number of sides from car 6 to car 19 = 19 - 6 = 13.

Therefore, the angle of rotation that maps car 6 to car 19 is given by

$\alpha=13\times \theta=13\times 20^\circ=260^\circ.$

Thus, the required angle of rotation is 260^\circ.