Question 46

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waecmaths question: 

The ratio of the exterior angle to the interior angle of a regular polygon 1:11. How many sides has the polygon? 

Option A: 

30

Option B: 

24

Option C: 

18

Option D: 

12

waecmaths solution: 

\[\begin{align}  & \text{Each angle in the exterior will be }\frac{{{360}^{\circ }}}{n} \\ & \text{Each angle in the interior angle }=\frac{(n-2){{180}^{\circ }}}{n} \\ & \text{The ratio is}\frac{\tfrac{360}{n}}{\tfrac{(n-2)180}{n}}=\frac{1}{11} \\ & \frac{360}{(n-2)180}=\frac{1}{11} \\ & \frac{2}{(n-2)}=\frac{1}{11} \\ & 22=n-2 \\ & n=24 \\\end{align}\]

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