Question

For a regular polygon the value of its interior angle is 5 times of its external angle , what is the number of sides?

Answer 1

Step-by-step explanation:

let the exterior angle be x and interior angle be 5x.

so,

Answer 2

Step-by-step explanation:

Given:-

For a regular polygon the value of its interior angle is 5 times of its external angle.

To find:-

what is the number of sides?

Solution:-

We know that

The interior angle of a regular polygon of 'n' sides=(n-2)×180°/n----(1)

The exterior angle of the regular polygon of 'n' sides=360°/n-----(2)

Given that

a regular polygon the value of its interior angle is 5 times of its external angle

= (n-2)×180°/n=5×(360°/n)

=>(n-2)×180°=5×360°

=>n-2=5×360°/180°

=>n-2=5×2

=>n-2=10

=>n=10+2

=>n=12

Answer:-

Number of sides in the given polygon=12