Question

How many sides does a regular polygon have if each of its interiar angle is 165

Answer 1

Answer:

Since the measure of each interior angle is

165

∘

,

165∘, we have

180

∘

(

n

−

2

)

n

=

165

∘

180

∘

(

n

−

2

)

=

165

∘

n

180

∘

n

−

360

∘

=

165

∘

n

180

∘

n

−

165

∘

n

=

360

∘

15

∘

n

=

360

∘

n

=

24

180∘(n−2)n=165∘180∘(n−2)=165∘n180∘n−360∘=165∘n180∘n−165∘n=360∘15∘n=360∘n=24

Hence, the regular polygon with interior angle each measuring 165 degrees is a 24-sided polygon.

Answer 2

Step-by-step explanation:

Let n be the number of sides of the regular polygon.

According to the Question,

$\frac{(n - 2)180}{n} = 165$

$180n - 360 = 165n$

$15n = 360$

$n = 24$

Hence , the number of sides of the regular polygon is 24.

I hope it helps you. If you have any doubts, then don't hesitate to ask.