Question

the sum of interior angles of a regular polygon is 7200. find the number of sides

Answer 1

let number of sides be n
asper fomula,
(2n-4)×90º = sum of all interior angles
BTP,
(2n-4) ×90º=7200º
(2n-4)=7200º÷90º
(2n)=80+4
n=84÷2
n =42
so,the polygon has 42 sides

Answer 2

Answer: The regular polygon given here has 42 sides.

Step-by-step explanation:

Given that:

• Sum of interior angles of the regular polygon is 7200.

Finding the number of sides:

Let the number of sides of polygon given be n.

We know that, the formula for the sum of all interior angles of a polygon:

• $s=(2n-4)*90^{0}$

Here s is given in the question, that is 7200.

• s=7200

Putting the value of s in the above formula, we get;

$(2n-4)*90^{0}=7200^{0}$

By solving;

$2n-4=7200/90$

$2n-4=80$

$2n=80+4=84$

So, $n=42$

Hence, the number of sides of the given polygon is 42 sides.