The ratio of an interior angle to an exterior angle of a regular polygon in 7:2. How many sides are there in this polygon?
Solution
Each Interior angle $= \left\{ \dfrac{2n -4}{n}\right\} \times 90^{\circ}$
Each Exterior angle $= \dfrac{360^{\circ}}{n}$
$\dfrac{\left\{ \frac{2n-4}{n}\right\} \times 90}{\frac{360}{n}} = \dfrac{7}{2} \Rightarrow n = 9$