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1. How many sides does a regular polygon have whose interior and exterior angle are in the ratio 2 : 1 ?

A. 3

B. 5

C. 6

D. 12

Solution:

Each exterior angle of n sided polygon is

= (\frac{360}{n})

And each interior angle of n sided polygon

\begin{aligned} = \frac{(n - 2) \times 180}{n} \\ ∴ \frac{\frac{(n - 2) \times 180}{n}}{\frac{360}{n}} = \frac{2}{1} \\ \Rightarrow \frac{(n - 2)}{2} = 2 \\ \Rightarrow n - 2 = 4 \\ \Rightarrow n = 6 \end{aligned}

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