Ive been given the following problem:
I was unable to figure out how to solve the problem, and I was told the answer was the following;
However, the program has failed to explain to me exactly how it got the answer... Looking online, I can only find solutions for single transversal, 2 line problems, which aren't necessarily difficult..
My question is, how exactly, piece by piece, do I find X given multiple transversals or parallel lines?
With more parallel lines or transversals you just apply the "Parallel lines cut transversals into proportional segments." theorem for more than once. (This theorem is essentially Thales' Theorem.)
I created an example in the figure below. Since you had successfully obtained $x=5$ from the lower trapezoid, we can write the following for the upper trapezoid. $$\frac{y}{3}=\frac{10}{x}=\frac{10}{5}\implies y=6$$