Question

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

Answer 1

Answer:24 sides

Step-by-step explanation:

You know that each of the interior angles is 165 degrees so that gives you half of your equation, 165 times n, or 165n. Second, set your interior angles equal to the interior angle formula (n-2)180 = 165n. Last, solve for n. Divide by 15 to get n = 24 sides to the polygon.

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 .