Quantitative Aptitude Ques 1784

Question: The ratio of the numbers of sides of two regular polygons is 1: 2. If each interior angle of the first polygon is $ 120{}^\circ , $ then the measure of each interior angle of the second polygon is

Options:

A) $ 140{}^\circ $

B) $ 135{}^\circ $

C) $ 150{}^\circ $

D) $ 160{}^\circ $

Show Answer

Answer:

Correct Answer: C

Solution:

  • Given, interior angle of the first polygon $ =120{}^\circ $ Let number of sides in first polygon be $ n _1 $ Then, $ \frac{n _1-2}{n _1}\times 180{}^\circ =120{}^\circ $

$ \Rightarrow $ $ 3n _1-6=2n _1 $
$ \Rightarrow $ $ n _1=6 $ $ \because $ Sides of the second polygon $ =6n=6\times 2=12 $

$ \therefore $ Interior angle of the second polygon $ =\frac{12-2}{12}\times 180{}^\circ =150{}^\circ $

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