Question

polygon find the number of sides of a regular polygon if it's each interior angle is 165
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Answer 1

$\huge{\bf{\underline{\purple{Solution :}}}}$

Let the number of sides in a regular Polygon = n

We know the formula of each interior angle of a Regular Polygon :

$\implies \bold{\frac{(n - 2) \ x \ 180^{\circ}}{n}}}$

∴

$\implies \bold{\frac{(n - 2 ) \ x \ 180^{\circ}}{n} = \bold{165}}$

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

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

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

$\implies \bold{ n = \bold{\frac{ 360^{\circ}}{15^{\circ}}}}$

n = 24

So, number of Sides of Regular Polygon n = 24 (Answer)

Polygon :

⇒A simple closed curve formed by one straight line segment is called Polygon.

⇒Polygon have two types :

1) Regular Polygon

2) Irregular Polygon

Answer 2

Step-by-step explanation:

Measure of each exterior angle = 180° − 165° = 15°

The sum of all exterior angles of any polygon is 360º.

Thus, number of sides of the polygon.

$\: \: \frac{360}{15} = 24$