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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