It's puzzle time again!

[N. W. Perry]

Basically I made a function that shall solve to 0 at the given angle

so given that:
angle ABC = angle CDE
BC+CD = 26

Right, except it's BAC and DCE in the picture, but no matter…

I took:
tan(ABC)= BC/36
BC=36*tan(ABC)

Got it, tan=O/A…

and then

CD= 8*cos(ABC)

And cos=A/H…

26 - 36*tan(ABC) = 8* cos(ABC)

so I made a graph for

f(ABC) = 26 - 36*tan(ABC) - 8* cos(ABC)

Of course, since the two sides are equal, subtract one side from the other to get zero…

then the term  get 0 we have a solution

So the solution is 0.483845377…? How does we get 27.7222764 degrees from that?

Sorry, I'm still slow with the algebra side of it!