The number of sides in two regular polygons are as 5 : 4 and difference between their angles is \[6{}^\circ .\]The number of sides in the polygons are [SSC (CGL) 2014] |
A) 12 and 15
B) 12 and 13
C) 20 and 16
D) 15 and 12
Correct Answer: D
Solution :
Let the number of sides of two regular polygons be \[5x\]and \[4x,\]respectively. |
\[\therefore \]Angle of polygons of sides \[5x=(2\times 5x-4)\] |
\[=(10x-4)\] |
and angle of polygons of sides \[4x=(2\times 4x-4)\] |
\[=(8x-4)\] |
Given that difference of their angles is 6. |
Then, according to the question, |
\[(10x-4)-(8x-4)=6\] |
\[\Rightarrow \] \[2x=6\]\[\Rightarrow \]\[x=3\] |
\[\therefore \]Sides of 1st polygon \[=5x=5\times 3=15\] |
Sides of 2nd polygon \[=4x=4\times 3=12\] |
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