Question

each interior angle of a regular polygon is 144° . find the interior angle of another regular polygon which has double the number of sides as the first polygon​

Answer 1

Step-by-step explanation:

Given:-

Each interior angle of a regular polygon is 144° .

To find:-

Find the interior angle of another regular polygon which has double the number of sides as the first polygon?

Solution:-

Given that

Each interior angle of a regular polygon is 144°

Let the number of the regular polygon be 'n'

We know that each interior angle of a regular polygon of'n'sides is [(n-2)/n]×180°

=>[(n-2)/n]×180° = 144°

=>(n-2)/n = 144°/180°

=>(n-2)/n = 4/5

On applying cross multiplication then

=>5×(n-2) = 4×n

=>5n -10 = 4n

=>5n -4n = 10

=>n = 10

Number of sides of the given polygon = 10

Given that

Number of second polygon = Double the number of sides in a first polygon = 2n

=>2×10 = 20

Each Interior angle of the regular polygon of 20 sides

=>[(20-2) /20]×180°

=>(18/20)×180°

=>(18×180°)/20°

=>18×9

=>162°

Answer:-

the interior angle of another regular polygon which has double the number of sides as the first polygon is 162°

Used formula:-

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