Question

The sum of the interior angles of a polygon is 2700 how many sides does it have

Answer 1

Answer = 17 sides

Step-by-step explanation:

Formula:

s = 180*(n-2)

s = the sum of the interior angles.

n = the number of sides of the polygon.  

s = 180*(n-2)

s = 2700

n = ?

2700 = 180*(n-2)  

$\frac{2700}{180} = \frac{180*(n-2)}{180}$

15 = n-2

15 + 2 = n - 2 + 2

17 = n

Answer 2

Given: The sum of the interior angles of a polygon is 2700

To find The number of sides this polygon has

Solution: The shape of two-dimensional figures in mathematics where the formation occurs as straight lines, is referred to as polygon.

We know that the sum of a polygon's interior angles, s = (n-2)×180°, where n= the polygon's number of sides.

Now from above s=2700

∴s=(n-2)×180°

⇒ (n-2)×180°=s

⇒(n-2)×180°=2700  [substituting the value os s]

⇒ n-2=2700/180

⇒ n-2=15

⇒ n=15+2  [∵if we change the sides, then the signs with the numbers are also changed]

⇒ n=17

Hence the number of sides this polygon has is 17.