(I'm Overwhelmed plan) Geometry Progress Quiz #7 (Question 8)

I understood Greg’s solution correctly but I used a different approach for this question and I wanted to understand what issue is there with that as I didn’t get the correct answer. I used the supplementary triangle property since there is one set of parallel lines, the angle adjacent to 135 can be derived by 180-135 which gives us 45 and since other two sides are equal that is 10, the angles opposite to it would be equal too so I assumed that as x.

To find x, we will do: 45+135+ 2x = 360
x = 90

Now, this is a bit weird value because it’s no longer a trapezoid so I wanted to know why is the supplementary angle property not applicable here?

Additionally, Is there any reliable website I could refer to understand all the properties of each polygon? In addition to the ones taught on website.

Thank you!

Can you send a diagram of your work? It’s kinda annoying/tedious having to do this in my head