Question

The sum of interior angles of a polygon is 2700 degree. how many sides this polygon has?​

Answer 1

$\large{\underline{\rm{\purple{\bf{Given:-}}}}}$

Sum interior angles of a polygon = 2700°

$\large{\underline{\rm{\purple{\bf{To \: Find:-}}}}}$

The number of sides this polygon have.

$\large{\underline{\rm{\purple{\bf{Solution:-}}}}}$

The sum of the angles of a regular polygon is given by,

$\boxed{\sf( n-2) \times 180^{o}=Sum \: of \: interior\: angles}$

Here,

$\sf n-2\times 180=2700$

'N' is the number of sides.

Since we have to find the number of sides, let's solve the value of 'n'

So, in this case

$\sf (n-2)\times 180^{o}=2700^{o}$

Then,

$\sf \dfrac{2700}{180} =n-2$

$\sf 15=n-2$

Finding the value of 'n'

$\sf n=15+2$

$\sf n= \underline{\underline{17 \: sides}}$

Therefore, the sides of this polygon have 17 sides.

Answer 2

Given : Sum of all interior angles of a polygon is 2700°

To Find :   Number of side

Solution:

Sum of all interior angles of a polygon = ( n- 2) * 180°

where n is number of sides

=>  ( n- 2) * 180° =  2700°

=> n - 2 = 15

=> n = 17

Number of sides = 17

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