undefined	undefined	undefined	undefined	$6$	$8$	undefined
undefined	${60}^o$	𝑜undefined	${36}^o$	𝑜undefined	𝑜30′undefined	${18}^o$

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Obliczenia:

 

$n=3$  

Kąt wewnętrzny trójkąta równobocznego to  ${60}^o$  

${180}^o={60}^o+2\beta$  

${120}^o=2\beta$  

${60}^o=\beta$  

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$n=5$  

Kąt wewnętrzny pięciokąta foremnego to  $\frac{5-2}{5}\cdot {180}^o=\frac{3}{5}\cdot {180}^o={108}^o$  

${180}^o={108}^o+2\beta$  

${72}^o=2\beta$  

${36}^o=\beta$    

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${30}^o=\beta$  

${60}^o=2\beta$  

${180}^o=\alpha +2\beta$  

${180}^o=\alpha +{60}^o$  

$\alpha ={120}^o$  

Kąt wewnętrzny ma miarę ${120}^o$  

$\frac{n-2}{n}\cdot {180}^o={120}^o\mid :{180}^o$  

$\frac{n-2}{n}=\frac{{120}^o}{{180}^o}$  

$\frac{n-2}{n}=\frac{2}{3}$  

$3\left(n-2\right)=2n$  

$3n-6=2n$  

$3n-2n=6$  

$n=6$  

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${22}^{o}30{}^{\prime }=\beta$  

${45}^o=2\beta$  

${180}^o=\alpha +2\beta$  

${180}^o=\alpha +{45}^o$  

${135}^o=\alpha$  

Kąt wewnętrzny ma miarę  ${135}^o$  

$\frac{n-2}{n}\cdot {180}^o={135}^o\mid :{180}^o$  

$\frac{n-2}{n}=\frac{{135}^o}{{180}^o}$  

$180\left(n-2\right)=135n$  

$180n-360=135n$  

$180n-135n=360$  

$45n=360\mid :45$  

$n=8$  

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$n=10$  

Kąt wewnętrzny dziesięciokąta ma miarę  $\frac{10-2}{10}\cdot {180}^o=\frac{8}{10}\cdot {180}^o=8\cdot {18}^o={144}^o$  

${180}^o={144}^o+2\beta$  

${36}^o=2\beta$  

${18}^o=\beta$