Question

IF THE RATIO OF THE INTERIOR ANGLE OF A REGULAR POLYGON IS 7:2, THEN THE NUMBER OF SIDES IS?

Answer 1

interior angle = 7t
exterior angle = 2t 
7t+2t=180   angle sum property 
9t=180
t=20 
so it shows that exterior angle =  t2
so on substituting the value of t we get exterior angle =  40 
so 
no of sides = 360 / exterior angle 
no of sides = 360/40 = 9 
so it has 9 sides 

Answer 2

Interior angle is 7x 
Interior angle is 2x 
So, 7x+2x= 9x = 180 
x= 20 
exterior  angle = 2*20 = 40
So, number of sides is 360/40 = 9