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Question -

Find the measure of each exterior angle of a regular polygon of
┬а(i) 9 sides (ii) 15 sides┬а



Answer -

Sum of angles a regular polygon having side n = (n-2)├Ч180┬░
(i) Sum of angles a regular polygon having side 9 = (9-2)├Ч180┬░= 7├Ч180┬░ = 1260┬░
Each interior angle=1260/9 = 140┬░
Each exterior angle = 180┬░ тАУ 140┬░ = 40┬░
Or,
Each exterior angle = sum of exterior angles/Number of angles = 360/9 = 40┬░

(ii) Sum of angles a regular polygon having side 15 = (15-2)├Ч180┬░
= 13├Ч180┬░ = 2340┬░
Each interior angle = 2340/15 = 156┬░
Each exterior angle = 180┬░ тАУ 156┬░ = 24┬░
Or,
Each exterior angle = sum of exterior angles/Number of angles = 360/15 = 24┬░

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