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Not really a big brain when it comes to math.

First question here... hope it meets the standards.

Let's say I've got a quadrilateral, I know the side lengths, and I know two of the sides are parallel. Can I figure out the angles?

m.a.a.
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  • Which angles do you mean? By definition, the internal angles of a rectangle are 90°, for instance? – sjb Jun 22 '16 at 11:45
  • "Rectangle" is the wrong word. It means a quadrilateral with all angles $90^o$. Presumably you must mean a quadrilateral (ie a figure with 4 sides). – almagest Jun 22 '16 at 11:45
  • In case you mean a trapezoid, the question is not trivial. Can you construct the trapezoid from the given sides? Hint If $AB$ and $CD$ are parallel, draw a parallel of $AD$ trough $C$. – Michael Hoppe Jun 22 '16 at 11:53
  • @almagest Sorry for that. Mixed up my English. Quadrilateral it is. – m.a.a. Jun 22 '16 at 14:04
  • @MichaelHoppe AB are parallel, but CD are not. I just know the sidelengths of all of them. – m.a.a. Jun 22 '16 at 14:19
  • @m.a.a. I refer $A$ to $D$ to be the edges of the trapezoid. – Michael Hoppe Jun 22 '16 at 21:06

1 Answers1

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A quadrilateral with 2 parallel sides is a trapezoid. Since you know all 4 side lengths you can calculate the length of the diagonals. Select one diagonal and find its length (e.g. use equation 10 in the above link). You now have 2 triangles where all side lengths are known. Finding angles in such triangles is easy.

Jens
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