The difference between any two consecutive interior angles of a polygon is 5 degree. If the smallest angle is 120 degree , How many sides the polygon have ?

• Sum of internal angle and external angle at any vertex of polygon is 180 deg.
  
  So largest exterior angle = 180-20= 60 deg.
  Sum of all external angles = 360 deg
  
  so external angles are 60,55,50,45,40,35,30,25,20 deg.
  
  hence 9 angles.
  so polygon has 9 sides.
• 12 years agoHelpfull: Yes(6) No(1)
• the polygon have 9 sides
  
  (n-2)180=120+125+..n terms=n/2(240+5n-5)
  
  180n-360=117.5n+2.5n^2
  
  2.5n^2 - 62.5n +360=0
  
  solving,
  n=9 is the answer.
  
  (We must discard the n=16 solution, because if n=16, the angles go past 180, and you can't have a 180 degree angle as an interior angle in a polygon)
• 12 years agoHelpfull: Yes(4) No(5)