Question

each exterior angle of the polygon is two third of its interior angles find the number of sites in a regular polygon.


explain and solve
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Answer 1

Step-by-step explanation:

$ext. \: angle = \frac{360}{no. \: of \: sides}$

$int. \: angle = \frac{(n - 2)180}{n}$

Here, n is the no. of sides of the polygon.

According to the Question,

$\frac{360}{n} = \frac{2}{3} \times \frac{(n - 2)180}{n}$

$\frac{360}{n} = \frac{120(n - 2)}{n}$

$n - 2 = 3$

$n = 5$

Hence , the number of sides of the polygon is 5.

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