Question : Each interior angle of a regular polygon is $18^{\circ}$ more than eight times an exterior angle. The number of sides of the polygon is:
Option 1: 10
Option 2: 15
Option 3: 20
Option 4: 25
Correct Answer: 20
Solution :
The sum of the exterior angles of a polygon = $360^{\circ}$
Let the number of sides of the regular polygon be $n$.
Each exterior angle = $\frac{360^\circ}{n}$
Each interior angle = $\frac{(n-2)\times 180^\circ}{n}$
According to the question,
$\frac{360^\circ}{n}\times 8 + 18^\circ=\frac{(n-2)\times 180^\circ}{n}$
⇒ $2880 + 18n =180n-360$
⇒ $n=\frac{3240}{162}=20$
Number of sides of regular polygon = 20
Hence, the correct answer is 20.
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