ANSWERS: 4
  • It depends if you are trying to find the interior or exterior angles. This website may help you. http://www.ul.ie/~cahird/polyhedronmode/hexagon.htm
  • i don't!
  • Imagine you are a turtle, following the edges of the polygon, with n sides, clockwise. Start somewhere on an edge. As you get to a vertex, you have to turn through an angle before continuing. When you get back to your starting position, and add up all the rotations, you're facing the same way: after n vertices you have rotated a full 360 degrees. The angle you turn each time is, therefore, 360/n. If instead when you reached a vertex you wanted to retrace your steps you would have to turn 180 degrees. Now suppose you've reached a vertex, and turned clockwise to your new heading (by 360/n), but NOW decide that you now want to retrace your steps. You've already turned 360/n, and have to turn through the interior angle of the polygon before you can retrace your steps. The second angle you turned, the interior angle of the polygon, is therefore 180 - 360/n Another way to do it: In the hexagon, join the vertices to the center. You made six equilateral (and eqiangled) triangles. Angles in a triangle add to 180. Each of the three angles in each triangle is therefore 180/3 = 60 degrees. You can get the interior angle of the hexagon just by looking at the diagram. For the octagon, draw the octagon so that it has two vertical and two horizontal sides. Use opposite horizontal and vertical sides to make a rectangle. The octagon is now made from five squares and four right-angled triangles. The right-angled triangles are also isoceles triangles with two equal angles. This gives you enough information to solve the interior angl efrom the diagram.
  • Hexagon:Join the centre to all vertices.You'll find 6 isosceles triangles formed.Now the angles of 6 traingles =6*180=1080 degrees. The angle around the centre of the hexagon = 360degrees so the sum of the angles of angles of the hexagon is 1080-360=720 degrees.Now the one angle = 720/6=120 degrees. Similarly replace for Octagon with 8 instead of 6. and the answer will be 135 degrees.

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