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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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