Find the smallest and greatest angle of a pentagon whose angle are in the ratio $6:3:2:5:4$.


Given: A pentagon.

To do: To find the smallest and greatest angle of a pentagon whose angle are in the ratio $6:3:2:5:4$.

Solution:

The ratio in the angles of a pentagon $6:3:2:5:4$.

Let $6x,\ 3x,\ 2x,\ 5x$ and $4x$ be the angles of given pentagon.
 
Sum of interior angle of a polygon $=180^o( n−2)$

Sum of angles of a pentagon $=180^o( 5−2)=540^o$       [$\because n=5$]
  
$\Rightarrow 6x+3x+2x+5x+4x=540^o$
 
$\Rightarrow 20x=540^o$

$\Rightarrow x=\frac{540^o}{20}$

$\Rightarrow x=27^o$

Therefore, smallest angle$=2x=2\times27^o=54^o$

Largest angle$=6x=6\times27=162^o$

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Updated on: 10-Oct-2022

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