Question : If the interior of a regular polygon is 170$^\circ$, then the number of sides of the polygon is:
Option 1: 36
Option 2: 20
Option 3: 18
Option 4: 27
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Correct Answer: 36
Solution :
Given: If the interior of a regular polygon is 170°.
Each interior angle of a regular polygon is given as $\frac{2n–4}{n}\times 90^\circ$ where $n$ is its number of sides.
So, $\frac{2n–4}{n}\times 90^\circ=170^\circ$
⇒ $\frac{2n–4}{n}\times 9=17$
⇒ $18n-36=17n$
$\therefore n=36$
Hence, the correct answer is 36.
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