Question

please help me!!!!!!!!!!!​

Answer 1

Step-by-step explanation:

Given :-

Each interior angle of a polygon is 180°

To find :-

Find the number of sides of the polygon ?

Solution:-

A regular polygon will never ever have an interior angle greater than or equal to 180°.

Check:-

Let the number of sides of the polygon be 'n'

We know that

The interior angle of a regular polygon of n sides

= [(n-2)/n]×180°

According to the given problem

Each interior angle of the polygon = 180°

=> [(n-2)/n]×180° = 180°

=> (n-2)/n = 180°/180°

=> (n-2)/n = 1

=> n-2 = 1×n

=> n-2 = n

=> n-n = 2

=> 0 = 2

But this is not true

So, We get contradiction.

Answer :-

A regular polygon will never ever have an interior angle greater than or equal to 180°.

Used formulae:-

The interior angle of a regular polygon of n sides

= [(n-2)/n]×180°