Question

Pls I want it urgently ​

Answer 1

Step-by-step explanation:

Solution :-

We know that

Each interior angle of a regular polygon of n sides is [(n-2)/n]×180°

Given that

Each interior angle of the regular polygon = 160°

=> [(n-2)/n]×180° = 160°

=> (n-2)/n = 160°/180°

=> (n-2)/n = 8/9

On applying cross multiplication then

=> 9(n-2) = 8n

=> 9n-18 = 8n

=> 9n -8n = 12

=> n = 12

The number of sides in the given regular polygon = 12

One third of 12 = 12/3 = 4

Now,

We have ,n = 4

Each interior angle of a regular polygon of n sides is [(n-2)/n]×180°

=>[ (4-2)/4]×180°

=> (2/4)×180°

=> 180°/2

=> 90°

Each interior angle = 90°

Answer :-

The number of sides in the given regular polygon =12

The interior angle of one third of the number of sides of the first polygon is 90°

Used formulae:-

→ Each interior angle of a regular polygon of n sides is [(n-2)/n]×180°