if the sides of a hexagon are in AP and the last most sides give an average of 160 degree then what is the average of the least most sides?

• 80 degree
  
  Sum of the interior angles of a hexagon is 720°.
  As the sides of hexagon are in AP, then its interior angles will also be in AP.
  Given, last most side has 160° and let least most side has angle of a° and difference between each angle=d° with number of sides n=6, then 160=a+(n-1)d
  Also sum of an AP, Sn=(n/2)[2a+(n-1)d]=(n/2)[a+a+(n-1)d]
  => 720=3(a+160)
  => a=80
• 6 years agoHelpfull: Yes(11) No(8)
• Answer=80 degree
  
  Sum of the interior angles of a hexagon is 720°.
  As the sides of hexagon are in AP, then its interior angles will also be in AP.
  So angle of triangle are a-3d, a-2d,a-d,a+d,a+2d,a+3d
  Sum of all interior angle of hexagon is 720.
  a-3d+ a-2d+a-d+a+d+a+2d+a+3d=720
  6a=720
  a=120
  last most side a+3d=160
  3d=40
  least most side a-3d=120-40=80
• 5 years agoHelpfull: Yes(4) No(1)
• how 80 has come plz explain
• 6 years agoHelpfull: Yes(0) No(0)
• sum of interior angles=720.
  ap and 6 sides given so sides will be a,a+d,a+2d,a+3d,a+4d,a+5d.
  therefore,a+5d=160(given).
  and sum of all sides that is,6a+15d=720.
  using these2 equations we get the smallest side that is a=80.
• 5 years agoHelpfull: Yes(0) No(0)