TITLE: Finding the sum of two angles
QUESTION [5 upvotes]: I gotta find the value of $x+y$ in the following image

I have no info about if a point is the middle point of a length or even the figure is a square. I can prove that
$$x-y=30°$$
And I tried to use similarity between triangles (and so, parallelism)  but I got no clue at all.

REPLY [2 votes]: Well I can prove that you can't find the answer without knowing if the figure is a square...Since you have the value for $x-y$ you need $2y$ so that you could add them up and get $x+y$...Even if you did something else and got $x+y$ what your essentially doing is finding $2y$ and adding it to $x-y$...Now think about the figure. Imagine the square or the rectangle being a bit longer in the horizontal direction...Then the contact point that makes the angle $x$, (contact point of the the right angle triangle that has $y$, with the square or the rectangle)  will be further away which in turn will increase the value of $y$ and $x$ equally (thats why $x-y$ is constant).
But since that increases $y$, $2y$ can't have a fixed value...And $x$ doesn't cancel out that increase in value of $2y$ cuz $x$ also increases
Sorry it looks like your question doesn't give you enough details...maybe its wrong...
I hope my proof proved that you can't possibly find the answer to this without knowing if thats a square or a rectangle