Question

the ratio of each interior angle to each exterior is 2:3 Find the number of sides in the polygon.​

Answer 1

$\huge\bf\mathfrak\blue{✫}$$\huge\bf\mathfrak{Required\: Answer}$

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$\bf\underline\mathfrak\blue{Given,}$

The ratio between the exterior angle and interior angle of a regular polygon is 2:3

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⇝ Each exterior angle of a regular

polygon = $\dfrac{180° ( n - 2 )}{n}$

⇝ when n = number of sides of polygon

⇝ Each exterior angle of a regular polygon = $\dfrac{360°}{n}$

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According to question,

$\dfrac{360°}{n}$ : $\dfrac{180° (n - 2)}{n}$

= 2:3

→ $\dfrac{2}{( n - 2 )}$ = $\dfrac{2}{3}$

⇝ n - 2 = 3

⇝ n = 5

Therefore, the number of

sides in the polygon is 5.

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Answer 2

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⇝ Each exterior angle of a regular polygon = 180°(n−2)/n

⇝ when n = number of sides of polygon

⇝ Each exterior angle of a regular polygon = 360°/n

According to question,

360°/n

180°(n−2)/n

= 2:3

→ 2/(n−2)

= ⅔

⇝ n - 2 = 3

⇝ n = 5

Ans. Therefore, the number of sides in the polygon is 5.