Question 22

If the measure of the interior angle of a regular polygon is 90° 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,

=> $$\frac{(n-2)\times180^\circ}{n}-\frac{360^\circ}{n}=90^\circ$$

=> $$180n-360-360=90n$$

=> $$180n-90n=720$$

=> $$n=\frac{720}{90}=8$$

=> Ans - (A)

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