the interior angle of a regular polygon is 156.how many diagonal does the polygon have?
option are 60 90 75 120

• Exterior angle = 180 - 156
  = 24 degrees
  
  Sum of exterior angles = 360 degrees.
  
  So one exterior angle = 360/24
  = 15 angles
  
  Therefore 15 edges.
  so from 15 edges there will be 90 diagonals
• 11 years agoHelpfull: Yes(31) No(2)
• Given : one Interior angle=156
  
  we know,for n polygon: each interior angle=(n-2)*180/n=156
  so, n=24...
  so diagonals can be drawn:(n^2-3n)/2
  =>(225-45)/2 =>90(ans)
• 11 years agoHelpfull: Yes(13) No(4)
• each interior angle=(n-2)180/n
  no of diagonal=n(n-3)/2
  here we can put (n-2)180/n=156
  so from this we find n=15
  now putting this val of n we get 1/2*15*(15-3)=90
  
• 11 years agoHelpfull: Yes(10) No(1)
• NO. OF SIDES,N
  ((N-2)/N)*180=156
  NO. OF DIAGONALS,
  NC2-N.. ANS 90
  
• 11 years agoHelpfull: Yes(4) No(0)
• for n polygon, each interior angle = (n-2)*180/n=156
  => n=15
  so diagonal = (n^2-3n)/2
  => diagonal is 90 Ans
• 11 years agoHelpfull: Yes(2) No(0)
• short cut to find number of diagonals in regular polygon is
  (n(n-3))/2
  where n is number of side
• 10 years agoHelpfull: Yes(0) No(0)