If there are maximum acute angles then how many convex hectagons are there?

• 3 hectagons
• 11 years agoHelpfull: Yes(3) No(5)
• plz provid options for this ques..pl urgent
• 11 years agoHelpfull: Yes(2) No(0)
• soumik explain the solution properly
• 11 years agoHelpfull: Yes(1) No(0)
• The sum of the interior angles of a hexagon is 720 degrees. In a convex polygon, each angle must be strictly less than 180 degrees.
  Six acute angles can only sum to less than 90deree* 6 = 540 degrees, so six acute angles could not form a hexagon.
  Five acute angles and one obtuse angle can only sum to less than 90deree* 5 + 180 = 630 degrees, so these angles could not form a hexagon.
  Four acute angles and two obtuse angles can only sum to less than 90deree* 4 + 180deree* 2 = 720 degrees. This is a strict inequality, so these angles could not form a hexagon. (The limiting figure would be four right angles and two striaght angles, which would really be a square with two "extra" points on two sides to form the straight angles.)
  Three acute angles and three obtuse angles work. For example, if you pick three acute angles of 80 degrees, the three obtuse angles would be 160 degrees and give a sum of 80deree* 3 + 160deree* 3 = 720 degrees, which is a genuine hexagon. Thus, the answer is 3
• 10 years agoHelpfull: Yes(1) No(0)
• what is a convex hectagon?
• 11 years agoHelpfull: Yes(0) No(1)
• Guys...ur calculations are correct...but afte getting 720...we must remember one thing...the question is how many hexagons form..so answer must be 1....angles alone 3
• 9 years agoHelpfull: Yes(0) No(0)