Triangle Problem

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 picture

Theta + a = 140 (since the angle of the side will be 180 total)
a + b = 160 (since the top triangle's internal angles make 180 total)
b + c = 130 (since the angle of the side will be 180 total)
c + Theta = 110 (since the center triangle will have 180 total)

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I would love for someone to prove me wrong, but you can't solve it with just those equations; I've tried it on my first attempt.
With those only those equations, the solution a = 85, b = 75, c = 55, theta = 55 is possible, but looking at the picture, clearly, c =/= theta.

EDIT: Oh, I didn't see that you used guess and check, but I'm just gonna point it out there that using substitution on those 4 equations will always get you 0 for whatever variable you decide to solve for first. The incorrect solution above was obtained from plugging the same equations into a matrix in my calculator. The correct answer of 30 is explained in my earlier post.