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I know the length of all 4 sides of a trapezium

I know that one of the angles is 90 degrees.

None of the sides are parallel to the others.

How can I determine the remaining 3 angels?

I know that one of the angles is 90 degrees.

None of the sides are parallel to the others.

How can I determine the remaining 3 angels?

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

Can you tell me which lengths make up the right angle?

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

- (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
- (North American English) (British English trapezoid) a flat shape with four straight sides, none of which are parallel

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

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

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

All you need is a protractor capable of measuring your angles with the precision required for your problem

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.

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For the convex case, draw the hypotenuse of the two sides that have the right angle. This gives you a right triangle and you can find those angles easily. Here is a link that shows you how to do that:

https://www.mathsisfun.com/algebra/trig-finding-angle-right-triangle.html

That hypotenuse line is a diagonal of your trapezium and it's formed two triangles one being the right triangle that you just worked on. Now you know the length of the hypotenuse using Pythagorean theorem. Now you are left with another triangle where you know the lengths of the three sides where one of them is the hypotenuse that you just calculated.

You can use the law of cosines to compute the three angles of the triangle. Here is a link that explains a lot of cosines:

https://en.m.wikipedia.org/wiki/Law_of_cosines