Question

How many sides does a regular polygon have if each of its interior angles is 165⁰?

Answer 1

Answer:

Let number of sides of given regular polygon is n.

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

S=(n−2)∗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)∗180=165n

180n−360=165n⇒15n=360⇒n=36015=24

So, number of sides in the given polygon is 24

Answer 2

Answer:

Each interior angle is 165°. Therefore, the number of sides of the regular polygon is 24.

Step-by-step explanation:

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