Question

find the no. of sides, if each interior angle of a regular polygon is 135°​

Answer 1

Answer:

each exterior angle = 180 - 135

= 45

no of sides = 360/ 45

= 8 sides

Answer 2

Question :-

find the number of sides if each interior angle of a regular polygon is 135 degree ?

Answer :-

the sum of the interior angle of a p-sided polygon is (p-2)×180°

so each angle of a regular P sided polygon is (p-2)/p×180°

So,

let n be the number of sides of a regular polygon whose interior angle are each 135 degree .

Now,

(n-2)n×180°

=> (n-2)/n×180°/180° =135°/180°

=> (n-2)/n=135°/180°

=> (n-2)/n= 3/4

=> n-2 /n×n =3/4n

=> n-2= 3/4n

=> n-2-3/4n+2=3/4n-3/4n+2

=> (1-3/4n)=2

=> (4/4-3/4)n= 2

=> (4-3)/4×n=2

So,

=> 1/4n=2

=> 1/4n×4=2×4

=> n= 8

So,p=8

Verification :-

(p-2)/p×180

=> (8-2)/8×180

=> 6/8×180

=> 3/4×180

=> 135°

Thanks