Question

how many sides does a regular polygon have if each of its interior angle is 165 ​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

24

Step-by-step explanation:

Let number of sides of given regular polygon is n.

Then, sum of all of the angles can be given as,

S=(n−2) x 180∘.... (1)

Also, as we are given each interior angle is 165∘,

So, Sum of all the angles will also be,

S=165n.... (2)

From (1) and (2),

(n−2) x 180=165n

180n−360=165n

⇒15n=360

⇒n=360/15

⇒n=24

So, number of sides in the given polygon is 24.

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