Question

He ratio between the exterior angle and the interior angle of a regular polygon is 1 : 3. Then the number of sides of the polygon is:

Answer 1

$\Large\underline\mathfrak{Question}$

The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 3. Then the number of sides of the polygon is ?

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$

$\green{\sf \: interior \: angle \: of \: regular\: polygon \: with \: sides \: n} \\ \\ \purple{\boxed{\bf\dfrac{(n - 2) \times 180}{n}}} \\ \\ \\ \sf \: exterior \: angle : - \\ \\ \red{\boxed{\bf\dfrac{360}{n}}}$

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$\underline {\underline{\LARGE{{\bf{\green{S}}}{\mathfrak{o}}{\mathfrak{\orange{l}}}{\mathfrak{\red{u}}}{\mathfrak{\pink{t}}}{\mathfrak{\purple{i}}}{\mathfrak{\blue{o}}}{\mathfrak{\red{n}}}}}} : \:$

we have To Find value of n .

Given Ratio = Exterior : Interior = 1 : 3

or,

→ (Exterior/interior) = 1/3

Putting values now we get,,

$\red{\boxed\implies} \: \dfrac{ \frac{360}{ \cancel{n}} }{ \frac{(n - 2) \times 180}{\cancel{n}} } = \dfrac{1}{3} \\ \\ \red{\boxed\implies} \: \: \dfrac{ \cancel{360}}{(n - 2) \times \cancel{180}} = \dfrac{1}{3} \\ \\ \red{\boxed\implies} \: \: \: \frac{2}{n - 2} = \frac{1}{3} \\ \\ \blue{\sf \: cross - multiply} \\ \\ \red{\boxed\implies} \: \: \: n - 2 = 6 \\ \\ \\ \pink{\large\boxed{\boxed{\bold{ \green{n} \orange= \red8}}}}$

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Hence, Number of Sides of Regular Polygon will be 8 ..

#BAL

#answerwithquality...

Answer 2

Answer:

Question

The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 3. Then the number of