Question 22

If a regular polygon has 10 sides then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

Solution

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

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

Thus, difference between measure of an interior and exterior angle, when $$n=10$$

= $$[\frac{(10-2)\times180^\circ}{10}]-[\frac{360^\circ}{10}]$$

= $$(8\times18^\circ)-(36^\circ)$$

= $$144^\circ-36^\circ=108^\circ$$

=> Ans - (D)

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