Question

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

Answer 1

Answer:

24

Step-by-step explanation:

We are given that each of the interior angles of a regular polygon is 165∘

Let us assume that the number of sides of a regular polygon is represented by n

We know that the measure of each interior angle of a regular polygon the formula is given by 180∘(n−2)n

Since the measure of each interior angle is 165∘

, we have

⇒180∘(n−2)n=165∘

Multiplying the above equation by n

on both sides, we get

⇒180∘(n−2)=165∘n⇒180∘n−360∘=165∘n

Adding the above equation with 360∘

on each side, we get

⇒180∘n−360∘+360∘=165∘n+360∘⇒180∘n=165∘n+360∘

Subtracting both sides by 165∘n

on both sides, we get

⇒180∘n−165∘n=165∘n+360∘−165∘n⇒15∘n=360∘

Dividing the above equation by 15∘

on each side, we get

⇒15∘n15∘=360∘15∘⇒n=24∘

Thus, the regular polygon with interior angle each measuring 165∘

is a 24-sided polygon.