Ex.2. An interior angle of a regula...
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Ex.2. An interior angle of a regular polygon is 5 times its exterior angle. Then the number of sides of the polygon is (1) 14 (2) 16 (3) 12 (4) 18

11th - 12th Class
Maths
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Sol. (3) If the number of sides of regular polygon be ( n, ) then Each interior angle ( =frac{(2 n-4) times 90^{circ}}{n} ) and each exterior angle ( =frac{360^{circ}}{n} ) ( therefore frac{(2 n-4)}{n} times 90^{circ}=frac{5 times 360^{circ}}{n} ) ( Rightarrow(2 n-4)=5 times 4 Rightarrow 2 n-4=20 ) ( Rightarrow 2 n=20+4=24 quad Rightarrow n=frac{24}{2}=12 )
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