Ex.3. Each interior angle of a regu...
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Ex.3. Each interior angle of a regular polygon is 18° more than eight times an exterior angle. The number of sides of the polygon is SSC CGL (Tier-1) 2011 (1) 10 (2) 15 (3) 20 (4) 25

11th - 12th Class
Maths
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Sol. (3) Let the number of sides of the regular polygon be ( n ), then ( thereforeleft(frac{2 n-4}{n}right) times 90^{circ} ) ( =8 times frac{4 times 90^{circ}}{n}+18^{circ} ) ( Rightarrowleft(frac{2 n-4}{n}right) times 5=frac{160}{n}+1 ) ( Rightarrow 10 n-20=160+n ) ( Rightarrow 10 n-n=180 ) ( Rightarrow 9 n=180 Rightarrow n=20 )
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