Question

How many sides does a regular polygon have if each of its interior angles is 165° ?

Answer 1

if each of its interior angles is 165°

Answer 2

Answer:

${\huge{\underline{\underline{\sf{\blue{Solution:-}}}}}}$

Let there be n sides of the polygon.

$then \: each \: interior \: angle \: = \: \frac{( n \: - \: 2) }{n}$

$therefore \: \frac{(n \: - \: 2) \: \times 180}{165}$

( n - 2) × 180 = 165n

=> 180 n - 360 = 165 n

=> 180n - 165n = 360 => 15n = 360

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

● The polygon has 24 sides .

${\huge{\underline{\underline{\sf{\blue{Alternate\: Method :-}}}}}}$

Each exterior angle = 180° - 165 ° = 15°

Let n be the number of sides .

n × 15° = 360 ( Exterior angle sum property )

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

Thus , the polygon has 24 sides .