Question 22

If the measure of the interior angle of a regular polygon is $$108^\circ$$ greater than the measure of its exterior angle then how many sides does it have?

Solution

Let the number of sides of the polygon = $$n$$

Sum of all interior angles = $$(n-2)\times180^\circ$$

Sum of all exterior angles = $$360^\circ$$

According to ques,

=> $$\frac{(n-2)\times180^\circ}{n}-\frac{360^\circ}{n}=108^\circ$$

=> $$180n-360-360=108n$$

=> $$180n-108n=720$$

=> $$n=\frac{720}{72}=10$$

=> Ans - (A)

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