Question

Find the number of sides of a regular polygon whose each interior angle is 135 degrees

Answer 1

Formula for sum S of  n interior angles  of n sided polygon is

S=(n−2)×180˚

Since polygon is regular all its interior angles is same, sum of them is 135 degree times n

So we have S=135n˚

As per formula,

S=(n−2)×180=135n˚˚

 180(n−2)=135n

180n−360=135n

 45n=360

 n=360/45=8

Number of sides is 8

Answer 2

Answer:

8

Step-by-step explanation:

Each interior angle=135°

Each exterior angle=180-135=45° [each interior angle =180-each exterior angle]

Let n be the number of sides, then

45*n=360°. [SUM OF ALL EXTERIOR ANGLE=360°]

n=360/45=8

Number of sides of the polygon =8