Do trapezium angles have to equal 360 degrees?

  1. The four sided, a=110.50 ft, b=165.27, c=162.18, and d=a slightly curved line of 146. ft--
    (from point to point, it still seems to be 146 feet,) anyway---This from a land survey---I believe the distances of width, center point and (height) can "prove" by the angles. The people I have been talking to claim it is a parallelogram. (professionals) and told me the corners have to add to 360 degrees---I will post an image. I am confused by the math of the people I have been speaking with.
     
  2. jcsd
  3. mgb_phys

    mgb_phys 8,952
    Science Advisor
    Homework Helper

    You can always draw a line to turn a four sided figure into 2 triangles.
    Since triangle's (on a flat plane) internal angles add to 180 and you have two of them - it must add to 360deg.
     
  4. I only know one angle. The angle of the 110.50 ft and the 165.27 feet, is stated to be
    121 degrees 11-----I tried to measure the lines on the survey to get the other angles--
    they appear to be, between the 165.27 ft and 162.18 ft -- 59 1/2 ----then between the 162.18 and the 146 ft., the angle of 102 1/2 then between the 146 ft and the 110.50 seems to be 76 1/2.--or if measured on the arc-not point to point, 78 1/2---I am still trying to locate this diagram file.
     
  5. attached a mini map shape----I am new here, hope it attaches to this post---I would like to be able to calc the angles from the distances shown, however, I seem to be
    blocked on this.
     

    Attached Files:

    Last edited: Oct 5, 2008
  6. mgb_phys

    mgb_phys 8,952
    Science Advisor
    Homework Helper

    What are actually trying to work out?

    ps if the two horizontal lines are parallel you are ok, otherwise you don't have enough information to calculate the area or angles. Picture it as four rods hinged at the ends, you can push them ito different shapes without changing the lenghts.
     
    Last edited: Oct 5, 2008
  7. Calculate the angles and from a centerpoint in the parallel line area of the diagram, draw a parallel line grid, (measured approx. 143 3/4 feet across) and then find the centerpoint distance from top to bottom. Then prove the distances from all sides and angles-like a line star.--My surveyor had asked me this question about the angles have to add up to 360 degrees, and I said yes-but I think I was wrong, including the curve, the angle total would have to be a couple of degrees more
     
  8. The four angles of any quadrilateral, i.e., 4-sided figures with straight line segments as sides, will add up to 360.

    However, your shape is concave-out along one side -- Hill-something-or-other-- so the angles will add up to something slightly larger than 360. I'm afraid that the only way to determine the actual angles along that side, is by straightforward surveying techniques. Do you have a sextant handy?
     
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