| 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 [SSC (CGL) Mains 2012] |
A) \[140{}^\circ \]
B) \[135{}^\circ \]
C) \[150{}^\circ \]
D) \[160{}^\circ \]
Correct Answer: C
Solution :
| Given, interior angle of the first polygon \[=120{}^\circ \] |
| Let number of sides in first polygon be \[{{n}_{1}}\] |
| Then, \[\frac{{{n}_{1}}-2}{{{n}_{1}}}\times 180{}^\circ =120{}^\circ \] |
| \[\Rightarrow \]\[3{{n}_{1}}-6=2{{n}_{1}}\]\[\Rightarrow \]\[{{n}_{1}}=6\] |
| \[\because \]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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