Determine remaining 3 angles of trapezium with 1 right angle.

As you know all sides length, you can determine the length of the diagonals. With these lengths you can use the trigonometric functions to determine the angles.

I have an Excel spread sheet that solves quadrilaterals.  

You can get it here:  https://www.experts-exchange.com/questions/29061368/Irregular-rectangular-area-calculation.html

Thanks for the input.  I lack a reasonable education in trig.   Could you provide the formula you have in mind?

trapezium, by definition:

1. (British English) (North American English trapezoid) a flat shape with four straight sides, one pair of opposite sides being parallel and the other pair not parallel
2. (North American English) (British English trapezoid) a flat shape with four straight sides, none of which are parallel

so are you using the North American or the British definition?

He is using north American since the op states that none of the sides are parallel to each other.

>>  I lack a reasonable education in trig.
Ok, here is a short video to show you the basics of the trig functions using a right triangle.

https://m.youtube.com/watch?v=X5uFqpypDy4

Now that you have become a little familiar with the basic trig functions , here is a video that shows you how to compute the angles of a right triangle:

https://m.youtube.com/watch?v=j4O3fpC4HFg

For the convex case you still have another triangle to compute the angles . Here is a video that gives an example of using the law of cosines. Shows how to find three angles of a triangle given known three side Lengths:
https://m.youtube.com/watch?v=xRnhvFCGrIk

Finally there is the case of the concave trapezium to consider, but this case can lead to some strange figures including something like a figure 8 as well as something like a quadrilateral that looks like it only has two sides. That's why I assumed the easier case where you have a convex trapezium. If you have a concave trapezium, I suggest addressing this in a separate question and giving the line lengths and draw a sketch of the figure so as to keep the problem solution unique.

Thanks a lot!

How about a solution using no math at all?
All you need is a protractor capable of measuring your angles with the precision required for your problem

The difficulty is that the responders were trying to help the questioner get the answer by working out steps suggested without just giving the answer. The questioner wanted just the answer.
Burr gets points because he pointed out that there was NO unique answer to the given problem and he offered a simple non-math answer which was ignored.
phoffric gets points because he provided lots of useful links and showed the steps necessary to get (eventually) the correct answer including the difficulty raised by burr.