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Question

Find the number of sides of a regular polygon if each of its interior angles is $$\dfrac { 3{ \pi  }^{ c } }{ 4 } $$.


Solution

Measure of each interior angle $$\dfrac{{3\pi }}{4}$$
$$ \Rightarrow \dfrac{{\left( {n - 2} \right)180}}{n} = \dfrac{{3\pi }}{4}$$
$$ \Rightarrow \dfrac{{(n - 2)}}{x} \times \pi  = \dfrac{{3\pi }}{4}$$
$$ \Rightarrow \dfrac{{\left( {n - 2} \right)}}{n} = \dfrac{3}{4}$$
$$ \Rightarrow 4n - 8 = 3n$$
$$\rightarrow n=8$$
Sy Number of sides is $$8$$

Mathematics

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