Question

the ratio of the exterior angle to be the interior angle of regular polygon is 2 ratio 7 how many sides does have the polygon have​

Answer 1

$\Large{\mathbf{\underline{\orange{Solution :-}}}}$

➮ let interior angle be 7x

➮ let exterior angle be 2x

$\large\mathbf\pink{7x + 2x = 180}$

$\large\mathbf\pink{9x = 180}$

$\large\mathbf\pink{x = \frac{180} {9} }$

$\begin{gathered}\color{purple}\boxed{ \bf{ x = 20}} \\ \end{gathered}$

Now,

$\large\rm \: 7x \\ 7 \times 20 \\ = 140$

$\large\rm \: 2x \\ 2 \times 20 \\ = 40$

$\large\sf \: exterior \: \: angle \: = \frac{360}{n}$

$\large\sf \: \frac{360}{40}$

$\large\sf \: n = 9$

Polygon has 9 sides hence it is a nonagon.

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Hope it helps

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