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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Number of sides of a regular polygon whose smallest angle of rotation is is 20. so correct option is 20.

Solution:

Need to determine sides of a regular polygon having smallest angle of rotation as

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

Number of sides of regular polygon

So for a regular polygon having central angle =

Number of sides =

Hence number of sides of a regular polygon whose smallest angle of rotation is is 20.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: