Question

Howmany sides does regular polygon have if each of its interior angle is 165°?

Answer 1

Answer:

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Answer 2

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Let the Sides of Regular Polygon be "n"

$\boxed {\bold{Each \: Interior \: Angle = \frac{(2n - 4) \times 90}{n} }}$

$\large\implies \bold{165 = \frac{(2n - 4) \times 90}{n} }$

$\implies \bold{165n = 180n - 360}$

$\implies \bold{360 = 180n - 165n}$

$\implies \bold{15n = 360}$

$\purple{\large\implies \bold{n = 24}}$

$\large\therefore$ That Regular Polygon has 24 Sides.

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