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

Answer:

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 = $\frac{360}{18} = 20$

Hence number of sides of a regular polygon whose smallest angle of rotation is $18^{\circ}$ is 20.