Question

If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have

O
4
O 10
O 12
O
20
O
24
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Answer 1

Number of sides of a regular polygon whose smallest angle of rotation is
`18^(\circ)` is 20. so correct option is 20.

Solution:

Need to determine sides of a regular polygon having smallest angle of rotation as
`18^(\circ)`

In above case smallest angle of rotation is same as central angle of regular polygon.

So now we need to determine number of sides of regular polygon whose central angle is
`18^(\circ)`

Number of sides of regular polygon
`= \frac{360}{\text {central angle}}`

So for a regular polygon having central angle =
`18^(\circ)`

Number of sides =
`(360)/(18) = 20`

Hence number of sides of a regular polygon whose smallest angle of rotation is
`18^(\circ)` is 20.