Resolving angle of parallelogram in 3D space

[Naton]

Hi there,

I'm doing a bit of amateur scale model making as a hobby, building shapes out of flat-cut pieces. Trigonometry is a huge help with this, but I've hit a snag where I'm trying to calculate the angle of a particular parallelogram so it fits with the rest of the geometry.

1. Homework Statement
I've mocked up all of the variables from my situation into the following diagram with the angle I'm trying to determine marked as x:

https://zirung-sn3301.files.1drv.com/y3mjpry3qkCccqFTsqO8r5FMSn5iW1EOxg8zIyxIwBWd-K9eOxx_xsxBwu3Jqhu9f4S4W5EPP40fJnMqGBNe_ld4sSOf2zYCl0gRIAsvEUn3f_Za9Wg1nwQVSdFTg8TN3ifwWz6V0saeSPCEGmylsD_qxfzYBPptIN1dp5gQdHsuj8/math.jpg

Homework Equations

The Attempt at a Solution

I have attempted to divide the shape into triangles so I can apply trigonometry to the problem, and even experimented with 3D trigonometry, however neither seemed applicable to finding a solution.
I know I haven't provided enough to deserve a full solution, but if anyone could point me in the direction of which mathematical principles I would need to study in order to solve this, I would be grateful and happy to read up on them and come back with my work (after all, I will need to do perform similar tasks in the future, so there's no point in just getting the answer to this one without learning to do it myself).

Thank you for your time,

-Naton

 

[andrewkirk]

I think the shape may be incompletely specified.
Call the parallelogram with the 65 and 115 degree angles P, and call the top right-angle triangle T.
Then the angle between the planes of T and P can change without disturbing any of the given measurements. We can visualize this with P being like a hanging sign that swings on hinges attached to the ##\sqrt{3}##-length side of T.
I think that, as that angle changes, the angle x will change.