In a regular polygon, the difference between the interior and exterior angle at any vertex is $108^{\circ}$. The number of sides is:

Question

Aicharya · Accepted Answer

Let exterior $= x$, interior $= 180 - x$. Then $(180-x) - x = 108 \Rightarrow 180 - 2x = 108 \Rightarrow x = 36^{\circ}$. So $n = \dfrac{360}{36} = 10$.

In a regular polygon, the difference between the interior and exterior angle at any vertex is $108^{\circ}$.…

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