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Each interior angle of a regular polygon is four times the exterior angle. Find the number of sides in the polygon.
Given: Each interior angle of a regular polygon is four times the exterior angle.
To do: To find the number of sides in the polygon.
Solution:
Let the number of sides$=n$
then, each interior angle$=\frac{( n-2)}{n}\times180$
As known, exterior angle$=\frac{360}{n}$
According to the question, $\frac{( n-2)}{n}\times180=4\times\frac{360}{n}$
$\Rightarrow ( n-2)\times 180=4( 360)$
$\Rightarrow n-2=\frac{4\times360}{180}$
$\Rightarrow n-2=8$
$\Rightarrow n=8+2=10$.
Thus number of the sides of the polygon is $10$.
Updated on: 10-Oct-2022
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