SOLUTION: I would like to solve the unknown angles of a trapezoid? I know the legs of the equal sided trapezoid and the angles total 180 degrees on each side (total 360 degrees, both sides).

Now draw two line segments from the endpoints of
the top side perpendicular to the bottom side, like
this:



So now we have the trapezoid divided into two
congruent right triangles on each side and a
rectangle in the middle. Since the top of the
rectangle is 10.75", the bottom is too. So
if we subtract the middle 10.75" from the
bottom side 58.75", we get

58.75" - 10.75" = 48".  That will be the
sum of the bottom sides of the two right
triangles, and since they are congruent,
each of the bottom sides of the triangle
will be 48" divided by 2 or 24".  So we
have this:



In the right triangle on the left, the adjacent
side to the angle marked A is 24" and the hypotenuse
is 39.75.  Therefore, since 

 

Using a calculator with the inverse cosine function,

angle A = 52.85935847° or 52°51'33.691" 

Edwin