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In a regular polygon of #n# sides, if exterior angle in degrees, is one-tenth the number of sides, find #n#?

Answer 1

Allison Allen

#n=60#

Sum of allthe exterior angles of any polygon is always #360^@#.

As it is a regular polygon of #n# sides and therefore all exterior angles are equal,

each exterior angle is #(360^@)/n#

and hence #(360^@)/n=n/10#

or #n^2=3600# i.e. #n=60#

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Answer 2

Sophia Alfred

The sum of the exterior angles of any polygon is always 360 degrees.

Given that the exterior angle of the polygon is one-tenth the number of sides, let's denote the exterior angle as ( \theta ). Thus, ( \theta = \frac{360}{n} ).

Given ( \theta = \frac{n}{10} ), we can equate the two expressions for ( \theta ):

[ \frac{360}{n} = \frac{n}{10} ]

To solve for ( n ):

[ 360 \times 10 = n^2 ]

[ 3600 = n^2 ]

[ n = \sqrt{3600} ]

[ n = 60 ]

So, the number of sides ( n ) in the regular polygon is 60.

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