Question

The measure of each interior angle of a regular polygon is 165'. Find the number of sides of polygon
​

Answer 1

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)∗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

number of sides of the polygon= 360/15 = 24