Question
Is it possible to have a regular polygon each of whose interior angles is 100°?
✓
Answer
Each interior angle of a regular polygon having n sides $=180-\Big(\frac{360}{\text{n}}\Big)=\frac{180\text{n}-360}{\text{n}}$
If each interior angle of the polygon is 100°, then:
$100=\frac{180\text{n}-360}{\text{n}}$
$\Rightarrow100\text{n}=180\text{n}-360$
$\Rightarrow180\text{n}-100\text{n}=360$
$\Rightarrow80\text{m}=360$
$\Rightarrow\text{n}=\frac{360}{80}=4.5$
If each interior angle of the polygon is 100°, then:
$100=\frac{180\text{n}-360}{\text{n}}$
$\Rightarrow100\text{n}=180\text{n}-360$
$\Rightarrow180\text{n}-100\text{n}=360$
$\Rightarrow80\text{m}=360$
$\Rightarrow\text{n}=\frac{360}{80}=4.5$
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