Question

Each interior angle of a regular polygon is three times its exterior angle, then the number of sides of the regular polygon is

Answer 1

sum of all interior angles of a regular polygon =(2n-4)*90 degrees

each interior angle =(2n-4)*90/n=say x....if exterior angle is y

, we have x+y=180..but we were given that interior angle(x)=thrice exterior angle(y) or....x=3y..hence x+y=3y+y=180..or 4y=180..or..y=180/4=45

hence interior angle =x=3y=3*45=135

so (2n-4)*90/n=135

180n-360=135n

180n-135n=360

45n=360

n=360/45=8

hence it is an octagon with 8 sides

hope this helps

plz mark brainliest