The exterior angle of a regular polygon is one-third of its interior angle. How many sides does the polygon have?
Solution
Let the interior angle of polygon be $x$.
the interior angle of polygon be $3x$.
$x + 3x = 180, x = 45^{\circ}$
Each exterior angle $= \dfrac{360}{n} \Rightarrow 45^{\circ} = \dfrac{360}{n} \Rightarrow n = 8$