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Each exterior angle of a regular polygon is 18 degrees. How many sides does the polygon have?

Answer 1

Autumn Armstrong

#20#

For a regular polygon with #n# sides, the exterior angle of any side is equal to

#"exterior angle"=(360˚)/n#

Thus, in this scenario,

#18˚=(360˚)/n#

Solve for #n#, the number of sides in the polygon.

#n(18˚)=360˚#

#n=(360˚)/(18˚)=20#

The polygon has #20# sides.

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Answer 2

Savannah Aguilar

The number of sides (n) of a regular polygon can be found using the formula:

[ n = \frac{360^\circ}{\text{exterior angle}} ]

Given that each exterior angle is 18 degrees, substituting into the formula:

[ n = \frac{360^\circ}{18^\circ} ]

[ n = 20 ]

So, the polygon has 20 sides.

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