$\alpha =\frac{\left(n-2\right)\cdot {180}^{\circ }}{n}\mid \cdot n$  

 

$n\cdot \alpha =\left(n-2\right)\cdot {180}^{\circ }$  

 

$n\cdot \alpha ={180}^{\circ }\cdot n-2\cdot {180}^{\circ }$  

 

$n\cdot \alpha ={180}^{\circ }\cdot n-{360}^{\circ }\mid -{180}^{\circ }\cdot n$  

 

$n\cdot \alpha -n\cdot {180}^{\circ }=-{360}^{\circ }$  

 

$n\cdot \left(\alpha -{180}^{\circ }\right)=-{360}^{\circ }\mid :\left(\alpha -{180}^{\circ }\right)$    

 

$n=\frac{-{360}^{\circ }}{\alpha -{180}^{\circ }}=\frac{\sout{\left(-1\right)}\cdot {360}^{\circ }}{\sout{\left(-1\right)}\cdot \left(-\alpha +{180}^{\circ }\right)}=\frac{{360}^{\circ }}{{180}^{\circ }-\alpha }$     

 

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$\alpha ={160}^{\circ }$    

 

$n=\frac{-{360}^{\circ }}{{160}^{\circ }-{180}^{\circ }}=\frac{-{360}^{\circ }}{-{20}^{\circ }}=18$