Question 810544
<pre>
I'm guessing your hexagon looks something like this:

{{{drawing(2400/7,400,-1,2.5,-.5,2.5,

locate(.7,.15,"130°"),locate(1.7,1.3,"75°"),locate(.4,1.85,"145°"),
red(arc(0,0,.9,-.9,130,180)),

line(0,0,-.64279,.76604),line(-.64279,.76604,-.38397,1.73197),

locate(-.39,1.7,"115°"),locate(-.6,.8,"125°"), locate(-.28,.17,"y°"),

 line(-.38397,1.73197,.60084,1.90562), line(.60084,1.90562,2.06755,1.27226),
line(2.06755,1.27226,1,0), line(1,0,-.8,0)  )}}} 

The sum of the interior angles of a polygon is (n-2)·180°.

A hexagon has 6 sides so n=6 and the sum of the interior angles is 

(6-2)·180° = 4·180° = 720°

The sum of the 5 given angles is 130°+75°+145°+115°+125° = 590°

So the remaing 6th interior angle is 720°-590° = 130°,
so we will label it 130° in red. 

{{{drawing(2400/7,400,-1,2.5,-.5,2.5,
red(locate(-.05,.15,"130°")),
locate(.7,.15,"130°"),locate(1.7,1.3,"75°"),locate(.4,1.85,"145°"),
red(arc(0,0,.9,-.9,130,180),arc(0,0,.65,-.6,0,130)),

line(0,0,-.64279,.76604),line(-.64279,.76604,-.38397,1.73197),

locate(-.39,1.7,"115°"),locate(-.6,.8,"125°"), locate(-.28,.17,"y°"),

 line(-.38397,1.73197,.60084,1.90562), line(.60084,1.90562,2.06755,1.27226),
line(2.06755,1.27226,1,0), line(1,0,-.8,0)  )}}}

And now y° and 130° are supplementary and have sum 180°.

Therefore y° = 180°-130° = 50° 

Edwin</pre>